16 de abril de 2025

Presentamos OpenAI o3 y o4-mini

Nuestros modelos más inteligentes y competentes hasta el momento, y con acceso completo a todas las herramientas

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Hoy lanzamos OpenAI o3 y o4-mini, los más recientes en nuestra serie o que presenta modelos entrenados para pensar durante más tiempo antes de responder. Estos modelos son los más inteligentes que hemos lanzado hasta la fecha y representan un cambio significativo en las capacidades de ChatGPT para todos los usuarios, desde los curiosos hasta investigadores avanzados. Por primera vez, nuestros modelos con capacidad de razonamiento pueden usar y combinar, de forma autónoma, todas las herramientas de ChatGPT. Es decir, pueden buscar en la web, analizar archivos cargados y otros datos con Python, razonar a fondo sobre las entradas visuales y hasta generar imágenes. Sin embargo, lo más importante es que estos modelos están entrenados para razonar sobre cuándo y cómo usar las herramientas para producir respuestas detalladas y bien pensadas en los formatos de salida adecuados para resolver problemas más complejos y generalmente en menos de un minuto. Esto les permite abordar preguntas multifacéticas de forma más efectiva, lo que supone un paso más hacia un ChatGPT más autónomo que pueda realizar tareas en tu lugar, de forma independiente. Al combinar el razonamiento más avanzado con el acceso completo a las herramientas, ofrecen un rendimiento significativamente más sólido en evaluaciones comparativas académicas y en tareas del mundo real que, a su vez, establece un nuevo estándar tanto en inteligencia como en utilidad.

¿Qué ha cambiado?

OpenAI o3 es nuestro modelo con capacidad de razonamiento más poderoso que amplía las fronteras de la programación, matemáticas, ciencia, percepción visual y más. Establece una nueva puntuación SOTA en evaluaciones comparativas como Codeforces, SWE-bench (sin tener que desarrollar una matriz específica para el modelo) y MMMU. Es perfecto para preguntas complejas que requieren un análisis multifacético y que tienen respuestas que pueden no ser inmediatamente obvias. En particular, se desempeña bien en tareas visuales como es el análisis de imágenes, tablas y gráficos. En las evaluaciones realizadas por expertos externos, o3 comete un 20 % menos de errores importantes que OpenAI o1 en tareas complejas del mundo real, y se destaca especialmente en áreas como programación, negocios/consultoría e ideas creativas. Los primeros evaluadores destacaron su rigor analítico como herramienta de pensamiento y enfatizaron su capacidad para generar y evaluar de forma crítica hipótesis novedosas, en especial, en contextos de biología, matemáticas e ingeniería.

OpenAI o4-mini es un modelo más pequeño, optimizado para tener una capacidad de razonamiento rápida y rentable. Es decir, logra un asombroso rendimiento para su tamaño y costo, en especial en tareas matemáticas, de programación y visuales. Es el modelo con mejor rendimiento en los exámenes AIME 2024 y 2025. En las evaluaciones realizadas por expertos, o4-mini también supera a su predecesor, o3‑mini, en tareas no relacionadas con las STEM, así como en áreas como la ciencia de datos. Gracias a su eficiencia, o4-mini es compatible con límites de uso más altos que los de o3, lo que lo convierte en una gran opción de alto volumen y alto rendimiento para las preguntas que requieren un mayor razonamiento.

Los evaluadores expertos externos consideraron que ambos modelos muestran una mejor capacidad para seguir instrucciones y ofrecen respuestas más útiles y verificables que sus predecesores, gracias a una mejor inteligencia y a la inclusión de fuentes web. En comparación con las iteraciones anteriores de nuestros modelos con capacidad de razonamiento, estos dos modelos también deberían poder tener conversaciones más naturales. Sobre todo, porque tiene como referencia a la memoria y a las conversaciones pasadas para que las respuestas sean más personalizadas y relevantes.

Modelos multimodales

Programación

Seguimiento de instrucciones y uso de herramientas autónomo

Todos los modelos se evalúan con configuraciones de “esfuerzo de razonamiento” elevadas, similares a variantes como “o4-mini-high” en ChatGPT.

Continuamos escalando el aprendizaje por refuerzo (RL)

Durante el desarrollo de OpenAI o3, observamos que el aprendizaje por refuerzo a gran escala presenta la misma tendencia de “más procesamiento = mejor rendimiento” que se demostró en el entrenamiento previo de la serie GPT. Y, al revisar el proceso de escalamiento en el RL, aumentamos aún más tanto el procesamiento del entrenamiento como el razonamiento al momento de la inferencia. Sin embargo, aún se observa un claro aumento en el rendimiento, lo que valida que el rendimiento de los modelos continúa mejorando cuanto más se les permite pensar. Así, con la misma latencia y costo que OpenAI o1, o3 ofrece un mayor rendimiento en ChatGPT. Además, validamos que, si lo dejamos pensar más tiempo, su rendimiento sigue aumentando.

También entrenamos a ambos modelos para que usen herramientas mediante el aprendizaje por refuerzo, lo que no solo les enseñó cómo usar herramientas, sino a razonar sobre cuándo usarlas. Su capacidad para implementar herramientas basadas en los resultados deseados los hace más capaces en situaciones con problemas abiertos, sobre todo en aquellas que involucran un razonamiento visual y flujos de trabajo de varios pasos. Esta mejora se ve reflejada en las evaluaciones comparativas académicas y en las tareas del mundo real, como lo informaron los primeros evaluadores.

Pensamiento con imágenes

Por primera vez, estos modelos pueden integrar imágenes directamente en su cadena de pensamiento. No solo ven una imagen, piensan con ella. Esto desbloquea una nueva clase de resolución de problemas que combina el razonamiento visual y textual, lo que se demuestra en su avanzado rendimiento en evaluaciones comparativas multimodales.

Los usuarios pueden cargar una foto de un pizarrón, un diagrama de un libro de texto o un boceto dibujado a mano, y el modelo puede interpretarlo, incluso si la imagen está borrosa, invertida o es de baja calidad. Además, con el uso de herramientas, los modelos pueden manipular imágenes al momento, y rotarlas, ampliarlas o transformarlas como parte de su proceso de razonamiento.

Estos modelos ofrecen la mejor precisión en tareas de percepción visual, lo que les permite resolver problemas que antes estaban fuera de su alcance. Conoce más acerca de la investigación sobre razonamiento visual en este blog⁠.

Avances hacia el uso autónomo de herramientas

OpenAI o3 y o4-mini tienen acceso completo a las herramientas de ChatGPT, así como a sus propias herramientas personalizadas a través de solicitudes de funciones en la API. Estos modelos están entrenados para razonar sobre cómo resolver problemas y para elegir cuándo y cómo usar las herramientas para producir respuestas detalladas y bien pensadas en los formatos de salida adecuados y generalmente en menos de un minuto.

Por ejemplo, un usuario podría preguntar: “How will summer energy usage in California compare to last year?” (¿Cómo será el consumo de energía en California este verano en comparación con el año pasado?) El modelo puede buscar en internet datos de servicios públicos, escribir un código en Python para crear un pronóstico, generar un gráfico o una imagen, y explicar los factores clave detrás de la predicción al concatenar múltiples solicitudes de herramienta. El razonamiento permite que los modelos reaccionen y se adapten dependiendo de la información que encuentren. Un ejemplo de esto es que pueden hacer varias búsquedas en internet con la ayuda de proveedores de búsqueda, revisar los resultados y realizar nuevas búsquedas si necesitan más información.

Este enfoque flexible y estratégico les permite a los modelos abordar tareas que requieren acceso a información actualizada que no está en su conocimiento integrado, a su razonamiento extendido, a su síntesis y a su generación de resultados en todas las modalidades.

Todos los ejemplos se llevaron a cabo con OpenAI o3.

OpenAI o3

Solve the following very hard math problem using your in-built knowledge of the literature:

Construct a degree 19 polynomial \ (p(x)) \ in \ mathbb{C}[x] such that \ (X := \ {\, p(x) = p(y) \, \} \ subset \ mathbb{P}^{1} \ times \ mathbb{P}^{1}\ ) has at least 3 (but not all linear) irreducible components over \ mathbb{C}. Choose \ (p(x)\ ) to be odd, monic, have real coefficients and linear coefficient \ (-19\ ) and calculate \ (p(19)\ ).

Razona sobre la construcción polinómica durante 55 segundos

The curve defined by p(x) = p(y) factors if p(x) is decomposable or has repeated factors. Actually, p(x)-p(y) always factors, and it’s divisible by (x-y). This gives one factor, and the rest is a degree d-1 polynomial in x and y. For the curve to have at least three irreducible components, p(x)-p(y) must factor into at least three nontrivial factors. Each factor corresponds to a component in projective space, and at least one must be nonlinear.
I’m checking the Dickson polynomials D_n(x,a) and focusing on their coefficients. With a=1, it seems the leading coefficient is always 1, confirming that Dickson polynomials are monic. The linear coefficient for odd n is following a predictable sign pattern: for n=19, it gives a coefficient of -19, which is exactly what I need. So the Dickson polynomial D_n(x,1) with odd n fits nicely with the linear coefficient I was looking for.
I've confirmed that the linear coefficient for p(x)=D19(x)p(x) = D_{19}(x)p(x)=D19(x) is correct, with the necessary scaling factor to match. Now for the next step, I need to compute D19(19)D_{19}(19)D19(19). Since Tn(z)T_n(z)Tn(z) grows quickly for real z>1z > 1z>1, I plan to compute this value using Python, leveraging the recurrence to avoid mistakes—it's going to be a big number. I'll make sure to present the numeric result neatly so it's understandable since the coefficients are integers.
The Dickson polynomial D_{19}(x,1) is confirmed to have the required properties: monic, odd, real coefficients, and a linear coefficient of -19. The factorization of D_{19}(x) into irreducible components is also verified and satisfies the condition of having at least 10 components (1 linear + 9 quadratics). To compute p(19), we'll use the recurrence relation for Dickson polynomials, but there's also a closed-form expression involving cosine that could be handy here. I'll proceed accordingly!
I confirmed the linear coefficient is working correctly, which means now I need to calculate p(19)=D19(19)p(19) = D_{19}(19)p(19)=D19(19). This involves evaluating T19(9.5)T_{19}(9.5)T19(9.5), which grows rapidly. To ensure I get an accurate result, I'll compute this using recurrence in Python. The result is a large number: 1,876,572,071,974,094,803,391,179. I'll use the commas to make it easier to read: p(19)=1,876,572,071,974,094,803,391,179p(19) = 1,876,572,071,974,094,803,391,179p(19)=1,876,572,071,974,094,803,391,179.
For a = 1, there’s a relationship between Dickson polynomials and Chebyshev polynomials: D_n(x, 1) = 2^(n-1) T_n(x/2). Checking this, we see that the definition of D_n(u + 1/u) aligns well with Chebyshev’s formula. By setting x = 2 cos(θ), we find that D_n(x) equals 2 T_n(x/2). Importantly, the leading coefficient works out to 1, confirming the identity holds. This is nice!
Now, I need to verify that p(x)−p(y)p(x) - p(y)p(x)−p(y) factors as desired, relying on the known Dickson polynomial factorization. According to the literature (like Fried and Jarden), the difference Dn(x)−Dn(y)D_n(x) - D_n(y)Dn(x)−Dn(y) factors into a product involving (x−y)(x - y)(x−y) and other expressions. I'll provide the explicit polynomial D19(x,1)D_{19}(x, 1)D19(x,1), list the coefficients, and explain how it satisfies the desired properties: monic, odd, etc. Lastly, I'll compute p(19)p(19)p(19).

Analyzed

Python

1from math import comb, cos, acos
2# Let's compute Dickson D_n(x,a=1) recursively
3def dickson(n,x,a=1):
4    if n==0:
5        return 2
6    if n==1:
7        return x
8    Dm2=2
9    Dm1=x
10    for k in range(2,n+1):
11        D= x*Dm1 - a*Dm2
12        Dm2, Dm1 = Dm1, D
13    return Dm1
14
15d19 = dickson(19,19,1)
16d19

1876572071974094803391179

Analyzed

Python

1d19

1876572071974094803391179

Analyzed

Python

1import locale, sys, math, json, textwrap, re, decimal

Analyzed

Python

1"{:,}".format(d19)

'1,876,572,071,974,094,803,391,179'

Analyzed

Python

1# compute coefficients of Dickson polynomial D_n(x,1) via recurrence polynomial representation
2from sympy import symbols, Poly
3
4x = symbols('x')
5def dickson_poly(n):

Poly(x**19 - 19*x**17 + 152*x**15 - 665*x**13 + 1729*x**11 - 2717*x**9 + 2508*x**7 - 1254*x**5 + 285*x**3 - 19*x, x,

Analyzed

Python

1poly19.as_expr()

x**19 - 19*x**17 + 152*x**15 - 665*x**13 + 1729*x**11 - 2717*x**9 + 2508*x**7 - 1254*x**5 + 285*x**3 - 19*x

Done

A convenient way to force many factors in
$p(x) \;-\; p(y)$ is to use a Dickson polynomial of the first kind.
For a parameter $a \in \mathbb{C}$ in math these are defined by

$D_0\!\left(x,\, a\right) = 2,\; D_1\!\left(x,\, a\right) = x,\; D_n\!\left(x,\, a\right) = x\,D_{n-1}\!\left(x,\, a\right) - a\,D_{n-2}\!\left(x,\, a\right)\quad (n \ge 2),$

and satisfy the functional identity

$D_n\!\left(u + \frac{a}{u},\, a\right) = u^{n} + \frac{a^{n}}{u^{n}}.$

1. Choosing the polynomial

Take $a = 1$ and $n=19$ .
Because $n$ is odd, $D_{19}\!\left(x,\, 1\right)$ is an odd polynomial; the recurrence immediately shows it is monic and has integer (hence real) coefficients.
The coefficient of $x$ is $x = (-1)^{\frac{n-1}{2}}\,n = -19,$ so all requested normalisations are satisfied.

Writing it out gives

$\boxed{% p(x) = D_{19}\!\left(x,1\right) = x^{19} - 19x^{17} + 152x^{15} - 665x^{13} + 1729x^{11} - 2717x^{9} + 2508x^{7} - 1254x^{5} + 285x^{3} - 19x% }\,.$

2. Irreducible components of $fX \;=\; \bigl\{\, p(x) = p(y) \,\bigr\}$

For Dickson polynomials one has the classical factorisation

$D_n\!\left(x,1\right) \;-\; D_n\!\left(y,1\right) \;=\; (x - y)\, \prod_{j=1}^{\frac{n-1}{2}} \Bigl( x^{2} + y^{2} - 2\cos\!\bigl(\tfrac{2\pi j}{n}\bigr)\,xy - 4\sin^{2}\!\bigl(\tfrac{\pi j}{n}\bigr) \Bigr),$

where each quadratic factor is irreducible over $\mathbb{C}$ (see, e.g., Lidl–Niederreiter, Finite Fields, §3.6).
For $n=19$ this gives

one linear component $x=y;$
nine quadratic components (corresponding to $\bigl(j = 1,\,\ldots,\,9\bigr).$

Hence $X \subset \mathbb{P}^{1} \times \mathbb{P}^{1}$ has $10$ irreducible components, at least three of them and not all linear, as required.

3. Evaluating $p(19)$

Using the recurrence (or the identity $D_n\!\left(x,\,1\right) \;=\; 2\,T_n\!\bigl(\tfrac{x}{2}\bigr)$ with Chebyshev $T_n$ one obtains

$p(19) \;=\; D_{19}\!\left(19,\,1\right) \;=\; 1\,876\,572\,071\,974\,094\,803\,391\,179.$

Thus the polynomial above fulfils every condition, and

$\boxed{% p(19) \;=\; 1{,}876{,}572{,}071{,}974{,}094{,}803{,}391{,}179 }.$

OpenAI o1

Solve the following very hard math problem using your in-built knowledge of the literature:

Razona durante 1 minuto y 19 segundos

I’m piecing together a degree 19 polynomial with only odd powers and a linear coefficient of -19, like: p(x)=x19+a17x17+…+a1xp(x) = x^{19} + a_{17}x^{17} + \ldots + a_1xp(x)=x19+a17x17+…+a1x.

I'm examining if the polynomial p(x)=x19+a17x17+…+a3x3−19xp(x) = x^{19} + a_{17}x^{17} + \ldots + a_3x^3 - 19xp(x)=x19+a17x17+…+a3x3−19x has a notable classical form, considering symmetry or factorization for multiple irreducible components.

To ensure p(x)p(x)p(x) has three or more irreducible components, I’m considering the factorization of p(x)−p(y)p(x) - p(y)p(x)−p(y) into at least three irreducible factors in C[x,y]\mathbb{C}[x,y]C[x,y].

I'm working through x19−y19x^{19} - y^{19}x19−y19 to ensure it balances linear and nonlinear factors, aiming for a polynomial with at least three irreducible components that aren't all linear.

Taking a closer look at how p(x)−p(y)p(x) - p(y)p(x)−p(y) can be factored into three distinct polynomials in xxx, aiming to achieve the desired irreducible components.

I'm thinking about how composing ppp with simpler polynomials, like xm−cx^m - cxm−c, could result in multiple irreducible components, achieving at least three distinct factors.

I’m exploring the factorization of p(x)−p(y)p(x) - p(y)p(x)−p(y) with cyclotomic polynomials. This method generates nnn linear irreducible factors, which might not achieve the required three distinct components.

I'm focusing on constructing an "odd" and monic polynomial, ensuring all exponents are odd and the leading term is x19x^{19}x19. This approach aims to achieve the desired factorization.

I'm working with the Chebyshev polynomials to ensure p(x)−p(y)p(x) - p(y)p(x)−p(y) has at least three irreducible components, leveraging their even or odd properties to manage coefficients.

Considering the odd Chebyshev polynomial T19(x)T_{19}(x)T19(x) for potential factorization, while also examining composite polynomials of lower degrees to enhance factorization properties.

I'm analyzing how a polynomial composed of lower-degree polynomials, like (x3−3x)k(x^3 - 3x)^k(x3−3x)k, could yield p(x)−p(y)p(x) - p(y)p(x)−p(y) with at least three irreducible components.

Piecing together polynomials with integer coefficients, like (x3−3x)k(x^3 - 3x)^k(x3−3x)k, to achieve factorization in p(x)−p(y)p(x) - p(y)p(x)−p(y) with at least three irreducible components, aiming for degree 19.

I’m examining how p(x)=(x3−3x)kp(x) = (x^3 - 3x)^kp(x)=(x3−3x)k or p(x)=x19−19xp(x) = x^19 - 19xp(x)=x19−19x might yield p(x)−p(y)p(x) - p(y)p(x)−p(y) with three irreducible components, focusing on ensuring the polynomial is of degree 19.

I’m analyzing p(x)−p(y)p(x) - p(y)p(x)−p(y) into (x−y)(x18+x17y+…+y18−19)(x-y)(x^{18} + x^{17}y + \ldots + y^{18} - 19)(x−y)(x18+x17y+…+y18−19) to identify irreducible components. The polynomial factor x18+x17y+…+y18−19x^{18} + x^{17}y + \ldots + y^{18} - 19x18+x17y+…+y18−19 remains challenging to factor further.

I’m thinking through a new approach: adjusting the Chebyshev polynomial T19(x)T_{19}(x)T19(x) to make it monic, aiming to achieve at least three irreducible components in p(x)−p(y)p(x) - p(y)p(x)−p(y).

OK, let's think through. I’m tweaking T19(x)T_{19}(x)T19(x)'s coefficients to keep the polynomial monic and check if it simplifies into multiple irreducible components.

I'm thinking over various factorization strategies for a monic polynomial of degree 19. The goal is to ensure at least one non-linear factor and achieve at least three irreducible components in p(x)−p(y)p(x) - p(y)p(x)−p(y).

I’m updating my approach to factor x2+xy+y2−1x^2 + xy + y^2 - 1x2+xy+y2−1 over complex numbers by exploring change of variables and third roots of unity. This helps in achieving the desired polynomial structure.

I'm combining x3−xx^3 - xx3−x with x19−19xx^{19} - 19xx19−19x to tweak the polynomial's coefficients and complexity, aiming to include more non-linear factors for the desired irreducibility.

Piecing together p(x)=x19−x3−19xp(x) = x^{19} - x^3 - 19xp(x)=x19−x3−19x to ensure it’s odd, monic, and has the required linear coefficient. This targets the desired irreducible factorizations.

I’m mapping out the second factor x18+…+y18−x2−xy−y2−19x^{18} + \ldots + y^{18} - x^2 - xy - y^2 - 19x18+…+y18−x2−xy−y2−19 to see if it can split into three irreducible components.

I’m considering methods to factorize the polynomial by making it divisible by x−yx - yx−y and ensuring the remaining factor splits into exactly two irreducible components, aiming for a less complex factorization.

I’m examining the polynomial x18+x17y+…+y18x^{18} + x^{17}y + \ldots + y^{18}x18+x17y+…+y18 and noting it simplifies to x19−y19x−y\frac{x^{19} - y^{19}}{x - y}x−yx19−y19, which might reveal further irreducible factors.

I’m mapping out the polynomial x(x18−1)−y(y18−1)x−y\frac{x(x^{18}-1) - y(y^{18}-1)}{x-y}x−yx(x18−1)−y(y18−1) for further factorization. This might yield just two irreducible components, which falls short of three.

I’m exploring whether the polynomial p(x)=x19−(x3)p(x) = x^19 - (x^3)p(x)=x19−(x3) can be expressed as the composition of a smaller polynomial with xkx^kxk, potentially revealing multiple irreducible components.

I'm examining if the polynomial T19(x)T_{19}(x)T19(x) can be factored using trigonometric identities, seeking partial factorization without fully linearizing, to gain multiple irreducible components.

OK, let me see. Trigonometric identities show multiple solutions for θ\thetaθ and ϕ\phiϕ, likely leading to 19 or 38 linear factors for T19(x)T_{19}(x)T19(x).

I’m examining how the equation arccos⁡x=±arccos⁡y+2kπ19\arccos x = \pm \arccos y + \frac{2k\pi}{19}arccosx=±arccosy+192kπ leads to possible multiple branches, potentially irreducible in the algebraic sense, and needing an example with at least three non-linear irreducible components.

OK, let me see. I’m pulling together details on the polynomial x3(x2−1)8+xx^3 (x^2 - 1)^8 + xx3(x2−1)8+x. It’s monic, with x19x^{19}x19 as the leading term, ensuring it meets key criteria.

I’m noting that the polynomial p(x)=x3(x2−1)8+xp(x) = x^3 (x^2 - 1)^8 + xp(x)=x3(x2−1)8+x is odd, with its linear coefficient patterning to -19.

I’m figuring out how to adjust the linear coefficient of polynomial p(x)p(x)p(x) to -19 by adding a constant factor ccc in front of xxx to ensure it’s adequately modified.

By tweaking the linear coefficient of p(x)=x3(x2−1)8+cxp(x) = x^3 (x^2 - 1)^8 + c xp(x)=x3(x2−1)8+cx to -19, it ensures the polynomial remains monic, odd, and real.

I’m working on adding a constant factor ccc to xxx in p(x)=x3(x2−1)8+cxp(x) = x^3 (x^2 - 1)^8 + c xp(x)=x3(x2−1)8+cx to ensure the linear coefficient is -19, making the polynomial monic, odd, and real.

I'm piecing together the polynomial p(x)=x3(x−1)8(x+1)8p(x) = x^3 (x-1)^8 (x+1)^8p(x)=x3(x−1)8(x+1)8 and considering how p(x)−p(y)p(x) - p(y)p(x)−p(y) might factor with factors like x−yx-yx−y.

I’m confirming p(x)p(x)p(x) is monic, odd, and real, with a linear coefficient of -19, by expanding x3(x2−1)8x^3 (x^2 -1)^8x3(x2−1)8 to set the constant ccc.

I found that for p(x) to have a coefficient of -19 for the x term, c must be -19. The polynomial, p(x), incorporates this constant and preserves the original polynomial's structure.

Below is one concrete example (over the reals) of an odd, monic, degree 19 polynomial with linear coefficient $-19$ whose zero-locus relation $\{\,p(x)=p(y)\,\}\ \text{in }\mathbb{P}^{1}\times\mathbb{P}^{1}$ splits into at least three irreducible components (and not all components are linear). We then compute $p(19)$ .

1. The polynomial

Consider

$p(x) \;=\; x^{3}\,\bigl(x^{2}-1\bigr)^{8} \;-\; 19x.$

We can expand

$x^{3}\,\bigl(x^{2}-1\bigr)^{8} \;=\; x^{19}\;-\;8x^{17}\;+\;28x^{15}\;-\;56x^{13}\;+\;70x^{11} \;-\;56x^{9}\;+\;28x^{7}\;-\;8x^{5}\;+\;x^{3}.$

Hence

$p(x) \;=\; x^{19} \;-\; 8x^{17} \;+\; 28x^{15} \;-\; 56x^{13} \;+\; 70x^{11} \;-\; 56x^{9} \;+\; 28x^{7} \;-\; 8x^{5} \;+\; x^{3} \;-\; 19x.$

Checking the required properties

Degree 19, monic:
The leading term is $x^{19}$ with coefficient $1$ .

Odd polynomial:
All exponents are odd $\bigl(19,\,17,\,\ldots,\,3,\,1\bigr),$ and the constant term is $0$ . Indeed,

$p(-x) \;=\; -\,p(x),$

which makes $p$ an odd polynomial.

Real coefficients:
All coefficients are real integers.

Linear coefficient $-19$ :
The coefficient of $x$ is clearly $-19$ .

At least three irreducible components, not all linear:
Over $\mathbb{C}$ , the locus

$X \;=\; \bigl\{\, (x,y) : p(x)=p(y) \,\bigr\} \;\subset\; \mathbb{P}^{1}\times\mathbb{P}^{1}$

factors in part because $p(x)$ has (for instance) the repeated factors $\bigl(x^{2}-1\bigr)^{8}$ in the big piece $x^{3}\,\bigl(x^{2}-1\bigr)^{8}$ . One sees that $\{\,p(x)=p(y)\,\}$ contains (at least) the divisor $${x=y\}$$ plus further factors coming from the roots $x = 0 \;\text{or}\; x = \pm 1,$ ensuring multiple irreducible components (and not all of them are hyperplanes).

2. Computing $p(19)$

A direct substitution $x=19$ gives a large integer. Symbolic expansion or a computer algebra system yields

$p(19) \;=\; 1934999285524070399999639.$

Hence the required value is

\boxed{\,p(19) \;=\; 1934999285524070399999639\,}. \] :contentReference[oaicite:0]{index=0}

OpenAI o3 obtiene la respuesta correcta sin usar la búsqueda web, mientras que o1 no puede ofrecer una respuesta correcta.

OpenAI o3

I own a boutique hotel chain with locations in Lisbon, Berlin, and London. I plan to expand into a new country in Europe, and a city in Asia, in 2026. What factors—such as tourism growth, seasonal occupancy patterns, and local economic indicators—best predict success? I want to be ahead of the curve and be in the next hot city before others. Pull regional travel data, economic statistics, and hotel occupancy rates; analyze trends visually and recommend ideal expansion locations.

Razona sobre la estrategia de expansión del hotel durante 1 minuto y 11 segundos

22 searches · 58 sources

We need to analyze tourism trends, economic data, and hotel occupancy rates for recommended cities. The focus is on expansion into a new European country and a city in Asia, with updated data and visualizations (via charts). To start, I’ll consider European cities like Athens, Valencia, or Prague—thinking about new markets, especially given the user already operates in Lisbon. Next, I'll gather relevant data for these cities and potentially an Asian location too, comparing factors like growth rates and occupancy trends to make the best recommendation.

Searched the web

2023 hotel occupancy rate Budapest STR report

2023 hotel occupancy rate Athens STR

News

STR

GTP Headlines

4 more

For the Asian location, I’m thinking about cities like Da Nang, Osaka, Chiang Mai, Penang, or Seoul. I'll need to choose one based on key factors. I'll gather data like occupancy rates and tourism arrivals from reliable sources, such as Eurostat, UNWTO, or STR Global. I’ll also need to generate charts to visualize these trends. I can simulate numbers for now, but I'll make sure to provide accurate figures, so I’ll check current data by browsing for source-specific statistics.

Searched the web

2024 hotel occupancy rate Zagreb 2024 STR

2024 hotel occupancy rate Valencia 2024

Cushman & Wakefield

Focus on Travel News

Travel and Tour World

7 more

Searched the web

nights spent tourist accommodation europe 2024 by region eurostat

European Commission

Reuters

For the Asian locations, I'll need to gather occupancy data for Osaka, Da Nang, Ho Chi Minh City, and Bangkok. These cities seem like key candidates to explore further. I’ll gather the relevant statistics and see how they compare in terms of tourism and hotel performance. Once I have the numbers, I can pull everything together clearly for analysis.

Searched the web

2024 hotel occupancy Tokyo 80% STR

2024 hotel occupancy Osaka STR 2024 average occupancy

2 more

I need to focus on one European city for expansion. Athens, Valencia, Warsaw, Budapest, Krakow, Dubrovnik, and Malaga are options, but let’s narrow it down to Athens or Valencia. Since the user wants a new country in Europe, Spain and Greece are strong contenders. Valencia has an 80-90% occupancy rate and solid economic indicators, while Athens shows strong growth in occupancy and RevPAR. In Asia, Osaka, Bangkok, and Da Nang are possibilities, but Osaka is seeing a tourism surge with about 76% occupancy.
For Asia, Bangkok has a 74% occupancy rate for H1 2024 with 35.5 million international arrivals, but Da Nang has strong growth, even though occupancy is at 60-65%. Osaka could be a good choice—it’s less saturated than Tokyo and offers lower land costs. Fukuoka is another possibility, but Osaka has solid data trends. To analyze this properly, we’ll include Athens, Valencia, Budapest, Osaka, Bangkok, and Da Nang in a chart. The visualization will compare occupancy, RevPAR growth, and tourism arrivals.
We have some estimated values for occupancy: Athens at 78%, Valencia at 85%, Budapest at 73%, Osaka at 74%, Bangkok at 74%, and Da Nang at 62%. Athens has a RevPAR growth of +11%, and Valencia is at +11.5%. Osaka should have high ADR, but we don’t have its RevPAR value—I'll focus on occupancy >76 and rate growth. For tourism arrivals, I estimated Athens’ airport growth at 14% YoY, but I should confirm exact details for Athens tourism arrivals in 2024.

Searched the web

Athens International Airport passenger growth 2024 vs 2023

Valencia airport passenger growth 2024 record

Osaka Kansai inbound tourism 2024 growth

AIA Media

javeamigos.com

News on Japan

7 more

We’ve got some useful airport passenger growth data now. To simplify, I’ll summarize the seasonal occupancy and other variables textually. I'll include key factors like GDP growth and unemployment for each city in a structured bullet-point format. For charts, I’m thinking of two bar charts: one for 2024 occupancy rate and one for tourism arrivals growth. I’ll also add a scatter chart for occupancy vs. passenger growth. I'll estimate values with disclaimers and provide citations for the numbers used.

Searched the web

Osaka RevPAR growth 2024 hotel market

Colliers

STR

HVS

4 more

I’ve confirmed occupancy numbers for Osaka (79%) and Bangkok (74%) while Da Nang’s occupancy for luxury hotels is around 60-65%, so it might not be ideal. Osaka stands out, especially with the upcoming Expo 2025. For each city, I’ll include occupancy, RevPAR growth, and passenger growth figures. I’ll also consider aspects like currency exchange and infrastructure. I’d better search for Budapest’s airport traffic growth so we can finalize our recommendations based on the most accurate data.

Searched the web

Budapest airport passenger traffic 2024 growth

DailyNewsHungary

BudAPPest

bud.hu

6 more

Searched the web

Budapest hotel occupancy 2024 average

Horwath HTL

Statista

HVS

5 more

Okay, Budapest's occupancy is tricky, but I found an Airbtics source showing 76% for short-term rentals, which may work. Alternatively, I could consider Warsaw, but the occupancy is similar to Budapest’s. For the European candidates, I’ll focus on Athens and Valencia and rank them. I also want to consider Osaka, Bangkok, and maybe Da Nang for Asia. Let me gather the numbers for the selected cities to create a proper table with occupancy, RevPAR, and passenger growth figures.
We have occupancy and growth approximations for each city—Osaka, Bangkok, Da Nang, and Athens. For Osaka, I'll use an estimated 18% growth in international visitors, though we don’t have exact data. Bangkok’s occupancy is 74%, with visitor growth up by about 25%. Da Nang's visitor growth is unclear, but we can estimate it at 12%. I'll focus on Athens, Valencia, Osaka, and Bangkok for reliability. Now, I'll create a DataFrame and visualizations to highlight key metrics more precisely.

Searched the web

Thailand international tourist arrivals 2024 35.5 million compared to 2023

TAT Newsroom

CBRE Commercial Real Estate Services

Your Guide To Thailand!

6 more

For Athens, we'll use an occupancy of 78% with 11.4% RevPAR growth and 13.1% passenger growth. Valencia will be at 73% occupancy (consistent with March 2025 data), 11.5% RevPAR growth, and 8.7% passenger growth. Osaka’s occupancy will be 79% with 8% RevPAR growth and an estimated 18% YOY visitor growth. Bangkok has 74% occupancy, a 6.6% RevPAR increase, and 26% passenger growth. I'll provide disclaimers about these estimates and build the DataFrame for comparison.

Analyzed

Python

1# Executing python code to import libraries

Done

How we picked the short‑list

To find the most “future‑proof” expansion targets we looked at three leading indicators that consistently predict hotel performance two‑to‑three years out:

Signal	Why it matters	Data we used (2024)
Average hotel occupancy	Captures real, in‑market demand after short‑term‑rental leakage and seasonality	STR, national hotel‑association and market‑consultancy releases
RevPAR growth YoY	Shows pricing power and room‑rate headroom; > 8 % is a strong sign of tightening supply	STR, Cushman & Wakefield, Colliers
Air‑passenger growth	A forward indicator of both leisure and MICE demand; airports expand only when airlines commit	Airport authority stats & ACI Europe/Asia reports

(Raw numbers and sources per city are cited inline below; two quick visual snapshots generated above for occupancies and the occupancy ▸ passenger‑growth relationship.)

European candidates

	Athens, GR	Valencia, ES	Budapest, HU
2024 avg. hotel occupancy	78 %	73 %	76 %
RevPAR growth (YoY)	+11.4 %	+11.5 %	+14 %
Air‑passenger growth (YoY)	+13.1 %	+8.7 %	+19 %
Why it’s hot next	Year‑round demand, coastal mega‑project (Ellinikon), still‑limited new‑hotel pipeline	Mediterranean lifestyle pivoting to tech/events; cruise‑to‑stay conversion lifting ADR	Expo‑style public spend, St Regis ’25, huge low‑cost‑carrier network driving demand
Key risks	Land‑price surge in historic core; ADR volatility if short‑lets regulated	Heavy summer seasonality; looming water‑usage levies	Forint swings; big 2025–26 room deliveries could soften rates

European pick

Athens edges out on balanced year‑round demand and double‑digit air‑passenger growth with still‑manageable land costs outside the historic triangle. Secure plots near the upcoming Ellinikon coastal park for differentiation.

Valencia is an excellent plan‑B if you prefer Spain’s regulatory/political stability.

Asian candidates

	Osaka, Japan	Bangkok, Thailand
2024 avg. hotel occupancy	79 % (H1; highest in APAC after Tokyo)	74 % (H1, +4.8 pp YoY)
RevPAR growth (YoY)	+8 % YoY; ADR USD 121 (+12 %)	+6.6 % YoY (nation‑wide; Phuket/BKK up)
Air‑passenger growth (YoY)	~18 % (14.6 m int’l visitors, record)	+26 % (35.5 m visitors, regional #1)
Why it’s hot next	Expo 2025 & integrated resort drive >25 m incremental visitors; weak yen = bargain for western tourists; limited green‑field plots within loop = boutique premium	Visa‑free China/India boosts arrivals, 5‑year airport expansion plan; mass‑market drives high occupancy, but boutique segment still niche around Charoenkrung & Ari
Key risks	High construction costs, tight labor; Expo bubble may cool 2027‑28	Heavy new‑build pipeline (22 k rooms 2024‑27); political swings & Baht strength could hit margins

Asian pick

Osaka wins on mega‑event upside, currency tailwinds, and still‑undersupplied high‑design boutique stock (most inventory is branded mid‑scale). Target mid‑rise heritage conversions in Nakanoshima & Kitahama before land prices spike pre‑Expo.

Bangkok remains a strong “fast‑follower” option if you want sheer volume and lower entry costs.

Key take‑aways & next steps

1. Athens + Osaka give you complementary seasonality (Mediterranean shoulder‑season fills vs. Japan’s cherry‑blossom & Expo peaks) and diversified currency exposure (EUR / JPY).

2. Both markets show >75 % occupancy and double‑digit demand growth—rare in a post‑recovery cycle.

3. Move quickly: scout 50‑80‑room heritage assets within Q3 2025; aim to open mid‑2026 to catch the Expo and Athens’ growing winter city‑break market.

4. Lock in long‑term fixed‑rate financing now; rising ADRs plus currency spreads improve real returns.

5. Build pre‑opening buzz via collabs with local cultural institutions (e.g., Osaka’s National Museum of Art; Athens’ SNFCC) to stand out from branded chains.

(Charts above: 2024 occupancy comparison and the occupancy ▸ passenger‑growth scatter—all underlying figures and sources listed in the tables.)

OpenAI o1

Razona sobre los factores de expansión del hotel durante 13 segundos

Assessing hotel expansion

Piecing together simulated data for city tourism and economic growth. Using Python and matplotlib, I'll rank these cities by potential expansion benefits. This approach helps envision future trends and makes a well-informed choice.

I'm creating bar and line charts using matplotlib to track tourism and occupancy trends in hypothetical cities across Asia and Europe. This approach highlights growth patterns clearly and effectively.

I’m crafting a detailed analysis to pinpoint the best cities for hotel expansion. Using Python, I’ll prioritize ones with the greatest projected tourism and occupancy growth.

Below is a sample data-driven approach to selecting new boutique hotel sites in Europe and Asia, based on factors like tourism growth, seasonal occupancy, and local economic indicators. Because we cannot access live data in this environment, the numbers below are fictional. However, the method for collecting, analyzing, and visually reviewing these data can be replicated with actual statistics from tourism boards, governmental economic data, and hotel industry reports (e.g., STR Global, CBRE, etc.).

1. Relevant Factors for Boutique Hotel Expansion

Tourism Growth & Demographics

Year-over-year (YoY) increase in inbound travelers.
Growth in specific travel segments: leisure vs. business vs. “bleisure.”
Demographics of travelers, especially for lifestyle-focused or design-oriented hotels.

Seasonal Occupancy Trends

High vs. shoulder vs. off-season trends.
Rate of occupancy fluctuations (i.e., is it consistent year-round or extremely seasonal?).

Local Economic Indicators

GDP growth forecasts (3-5 years).
Levels of private investment and new developments.
Stability of local government, taxation, or real estate regulations impacting tourism/hospitality.

Competition / Market Saturation

Existing boutique hotels: supply vs. demand.
Average daily rate (ADR) or RevPAR (Revenue per available room) trends.

Infrastructure & Accessibility

Availability of international flights, airport capacity, rail connectivity.
Local attractions, business hubs, events, and conferences that draw travelers.

2. Sample Data and Analysis

Below, we create fictional data sets for five European and five Asian cities as an illustration. Suppose we’ve gathered:

Tourism Growth (YoY %) from 2022 to 2023 (proxy for short-term trajectory),
Projected GDP Growth (3-year avg.) as a measure of medium-term economic health,
Average Occupancy Rate (%) for hotels (2023),
Average Daily Rate (ADR) in USD as a proxy for market yield potential.

We then visualize these data in separate charts. Use a similar approach with real numbers from reputable data sources when finalizing an expansion decision.

2.1. Sample European Cities Data

Let’s say we consider five up-and-coming European cities:

City	Tourism Growth (YoY %)	Projected GDP Growth (3-yr)	Avg. Occupancy Rate (%)	ADR (USD)
Amsterdam	8.0	2.2	79	180
Prague	10.5	3.1	71	120
Barcelona	9.0	2.5	75	160
Budapest	11.0	3.5	68	100
Warsaw	7.5	3.8	65	95

2.2. Sample Asian Cities Data

For Asia, consider a short list of growing tourism hubs:

City	Tourism Growth (YoY %)	Projected GDP Growth (3-yr)	Avg. Occupancy Rate (%)	ADR (USD)
Bangkok	12.5	3.0	70	90
Ho Chi Minh	14.0	4.2	68	75
Tokyo	5.0	1.8	83	220
Kuala Lumpur	13.0	3.5	67	85
Seoul	6.5	2.2	80	140

3. Visualizing the Trends

Below is Python code that simulates creating these data frames, then plotting bar charts for each region. In practice, you would replace the fictional numbers with real data.

Python

1import matplotlib.pyplot as plt
2import pandas as pd
3
4# --- 1) Create fictional data for Europe ---
5european_data = {
6    'City': ['Amsterdam', 'Prague', 'Barcelona', 'Budapest', 'Warsaw'],
7    'Tourism Growth (YoY %)': [8.0, 10.5, 9.0, 11.0, 7.5],
8    'Projected GDP Growth (3-yr)': [2.2, 3.1, 2.5, 3.5, 3.8],
9    'Avg. Occupancy Rate (%)': [79, 71, 75, 68, 65],
10    'ADR (USD)': [180, 120, 160, 100, 95]
11}
12df_europe = pd.DataFrame(european_data)
13
14# --- 2) Create fictional data for Asia ---
15asia_data = {
16    'City': ['Bangkok', 'Ho Chi Minh', 'Tokyo', 'Kuala Lumpur', 'Seoul'],
17    'Tourism Growth (YoY %)': [12.5, 14.0, 5.0, 13.0, 6.5],
18    'Projected GDP Growth (3-yr)': [3.0, 4.2, 1.8, 3.5, 2.2],
19    'Avg. Occupancy Rate (%)': [70, 68, 83, 67, 80],
20    'ADR (USD)': [90, 75, 220, 85, 140]
21}
22df_asia = pd.DataFrame(asia_data)
23
24# --- 3) Bar Chart: Tourism Growth (Europe) ---
25plt.bar(df_europe['City'], df_europe['Tourism Growth (YoY %)'])
26plt.title('Tourism Growth (YoY %) - Europe')
27plt.xlabel('City')
28plt.ylabel('Tourism Growth (YoY %)')
29plt.show()
30
31# --- 4) Bar Chart: Avg. Occupancy Rate (Europe) ---
32plt.bar(df_europe['City'], df_europe['Avg. Occupancy Rate (%)'])
33plt.title('Average Occupancy Rate (%) - Europe')
34plt.xlabel('City')
35plt.ylabel('Occupancy Rate (%)')
36plt.show()
37
38# --- 5) Bar Chart: Tourism Growth (Asia) ---
39plt.bar(df_asia['City'], df_asia['Tourism Growth (YoY %)'])
40plt.title('Tourism Growth (YoY %) - Asia')
41plt.xlabel('City')
42plt.ylabel('Tourism Growth (YoY %)')
43plt.show()
44
45# --- 6) Bar Chart: Avg. Occupancy Rate (Asia) ---
46plt.bar(df_asia['City'], df_asia['Avg. Occupancy Rate (%)'])
47plt.title('Average Occupancy Rate (%) - Asia')
48plt.xlabel('City')
49plt.ylabel('Occupancy Rate (%)')
50plt.show()
51

4. Interpreting the (Sample) Results

Europe
- Budapest and Prague show strong Tourism Growth and moderate Occupancy Rates. GDP growth projections are also relatively strong. These indicators suggest that the market for boutique hotels might be on the rise, potentially less saturated compared to major hubs like London, Berlin, or even Amsterdam.
- Warsaw shows a good GDP growth rate but a slightly lower current occupancy. This could mean a growing market that’s not fully tapped yet—potentially favorable for an early move.
Asia
- Ho Chi Minh and Kuala Lumpur show robust Tourism Growth and decent GDP projections. Their ADR (Average Daily Rate) is lower than Tokyo or Seoul, meaning it’s more affordable but with a potentially fast-rising market.
- Tokyo has a high occupancy rate and high ADR—very established but also highly competitive and potentially costly.
- Bangkok remains a strong tourism hub with continued double-digit tourism growth. However, it’s also known for well-established competition.

Based on these (fictional) charts, a boutique hotel chain looking to be ahead of the curve might find:

Budapest (Europe) offers rising tourism, moderate but improving occupancy, and a relatively affordable market.
Ho Chi Minh City (Asia) demonstrates a fast-growing economy, strong tourism increases, and still-moderate ADR—indicative of an emerging market.

5. Practical Steps for Real Data Analysis

1. Gather Official Statistics

Tourism boards, national statistical agencies, hotel associations (e.g., STR Global).
Data on inbound traveler numbers, hotel performance indexes, and pipeline reports on new hotels.

2. Examine 3-5 Years of Historical and Forecast Data

Identify upward or downward trends in arrivals, occupancy, and ADR.
Check local economic forecasts from reputable sources (IMF, World Bank, national banks).

3. Competitive Analysis

Look at how many new boutique hotels are opening in the next 2-3 years.
Are major hospitality players entering the same market?

4. On-the-Ground Insights

Visit the cities if possible, talk to local tourism boards, real estate developers, and potential partners.
Evaluate property availability, local partnerships, and regulatory details.

5. Develop a Weighted Score

Assign a weight to each factor (tourism growth, GDP, occupancy, infrastructure, etc.).
Rank prospective cities, but also consider your brand’s positioning (luxury, design-forward, mid-scale boutique, etc.).

6. Conclusion & Recommendation

Ideal European Expansion: Cities like Budapest, Prague, or Warsaw may offer excellent growth potential without the saturated competition and high costs of Western European capitals.
Ideal Asian Expansion: Ho Chi Minh City or Kuala Lumpur could offer strong demand growth, favorable costs, and less-saturated markets compared to Tokyo or Seoul.

The final decision should blend quantitative data (e.g., occupancy rates, market growth, economic forecasts) with qualitative factors such as brand alignment, guest demographics, and the local cultural fit for a boutique experience.

Important Disclaimer

All numeric data provided here is illustrative and fictitious, intended to demonstrate how you might visualize and interpret real-world metrics. For an actual expansion decision, use verified, up-to-date data sources and do more detailed on-the-ground due diligence.

OpenAI o3 cita fuentes más relevantes para el sector y ofrece un plan que se basa más en los datos, es más exhaustivo y cuenta con más información estratégica, al mismo tiempo que anticipa los desafíos del mundo real y ofrece mitigaciones proactivas.

OpenAI o3

What impact did recent breakthroughs in battery technology have on electric vehicle range, charging speed, and adoption rates compared to previous generations? Gather relevant scientific studies, industry adoption data, and technical specifications; create visual comparisons, and summarize key scientific advancements.

Razona durante 40 segundos

17 searches · 26 sources

There are numerous recent breakthroughs in battery technology, such as silicon anodes, solid-state batteries (like those from Toyota and QuantumScape), and advancements in lithium iron phosphate (LFP) tech from companies like CATL and BYD. Additionally, there's progress with sodium-ion and lithium-metal batteries. These technologies are greatly improving EV ranges — for example, the 2012 Nissan Leaf had a 117 km range compared to the 2024 Tesla Model S LR with over 650 km. I’ll make sure to illustrate these improvements with a chart.
Charging speeds have drastically increased: early DC fast chargers offered 50 kW, while now we see 250-350 kW chargers, with some 4C cells. For adoption, EV global sales have grown significantly, partly due to improved battery technology. I’ll gather sources like studies on solid-state batteries and CATL’s Shenxing LFP cells. Then, I’ll create charts comparing EV range, charging speeds, and adoption growth from 2012-2023, using sources like the IEA Global EV Outlook and vehicle data for comparison.

Searched the web

IEA Global EV Outlook 2024 electric car sales 2023

CATL Shenxing LFP 4C charging 2023 range 700 km 10 minute charging

7 more

I'll summarize EV data, using range milestones, such as the Nissan Leaf’s 73 miles (2011) and Lucid Air’s 516 miles (2024). For charging power, example figures would show CHAdeMO at 50 kW (2011) and CATL’s Shenxing 4C cell at 480 kW (2023). EV adoption has drastically grown too — from 0.1M in 2011 to 40M in 2023, according to IEA data. Three line charts will visualize this. I also need to highlight major breakthroughs in battery technology, including high-silicon anodes and solid-state electrolytes.
I need to include academic studies like Nature Energy 2023 on lithium-metal solid-state and the Journal of Electrochemical Society 2024 on silicon anode cycling, along with research from UL or Argonne. I'll structure this content starting with an introductory paragraph, followed by key scientific breakthroughs in bullet points (with citations). I’ll then create charts using Python, interpret them (range, charging speed, and adoption), and summarize how battery improvements lead to quicker adoption. Finally, I’ll conclude. I’ll ensure the tone is structured yet conversational, with concise and detailed sections.
Next, I'll generate visual comparisons, including charts showing range increases, charging speed improvements, and adoption trends using Python. The data will highlight how battery improvements directly drive EV adoption. I’ll already have range and adoption data, but I’ll need a bit more info on charging speeds, like CHAdeMO 50 kW from 2011 with the Nissan Leaf. I'll search for trends in average EPA ranges and charging speed advancements to complete the analysis. I’ll make sure to keep it concise but still detailed!

Searched the web

average EPA rated electric vehicle range year 2011 2024

Inside EVs

US EPA

U.S. Department of Energy

3 more

Searched the web

2011 Nissan Leaf CHAdeMO 50 kW charging speed

Tesla Supercharger V1 120 kW 2013

Electrly

EV Chargers Guide

Taycan Forum

4 more

I’m looking for more data on average EV range and charging speeds to better illustrate trends. I've got sources for range and adoption, but I need a site summarizing the average EPA range over the years. For charging speeds, I should verify with sources like the 2011 CHAdeMO 50 kW rate for the Nissan Leaf and maybe also check the DOE's data on median EV range for 2011. Once I confirm the details, I'll move ahead with the visuals and analysis.

Searched the web

median EV range 2011 DOE fact of the week

U.S. Department of Energy

Hydrogen Program

I’m collecting sources for average EV range and adoption. I have enough data for range trends, including EPA figures and adoption rates. I’ve also found sources for charging speeds, like the CHAdeMO 50 kW rate for the 2011 Nissan Leaf. I'll shift focus to search for DOE's median EV range data from 2011 to complete the dataset. With that, I’ll be ready to begin analyzing and presenting the trends. Let's keep this concise and effective!
I’ve gathered enough adoption data, including IEA 2024 and OurWorldInData sources. It seems I'm set there. For scientific studies, I’ve got Nature Energy and Sila for solid-state and silicon anodes. I might look into sodium-ion battery research next. So, with solid data on range, charging speed, and adoption, the next step is visual comparisons. I’ll build three charts: featuring trends like the median EV range over time (2011, 2014, 2018, 2024), using DOE data like Fact of Week #1064 and #1375.

Searched the web

CATL sodium-ion battery EV 2023 energy density 160 Wh kg

Ev Specifications

Ars Technica

CATL

4 more

Done

What the data show at a glance

Range ↑ ~4× (2011 → 2024) – The U.S. median EPA‑rated range climbed from 73 mi in 2011 to 283 mi in 2024.
energy
Fast‑charging power ↑ ~8× – Mainstream EVs moved from 50 kW CHAdeMO on the first‑gen Nissan Leaf to 350 kW 800‑V platforms (e.g., Hyundai Ioniq 5) and 4 C‑capable cells such as CATL’s Shenxing (≈400 kW equivalent).
Adoption ↑ ~70× – Global sales grew from ≈0.2 M in 2013 to ≈14 M in 2023; one in five new cars sold last year was electric, lifting the global fleet above 40 M.

(Interactive charts and the underlying tables are shown above.)

Key scientific breakthroughs driving the gains

Breakthrough	Core idea	Impact on range / charge	Representative study or demo
High‑silicon anodes	Replace part of graphite with nano‑engineered Si to ↑ capacity	+20‑40 % energy density; 15‑min 80 % charges demonstrated	Sila “Titan Silicon” anode entering Mercedes EQG pack; REC‑Sila silane deal 2024
Solid‑state / lithium‑metal	Solid electrolyte eliminates flammable liquid; enables Li‑metal anode	Lab cells > 500 Wh kg⁻¹, 80 % in < 15 min, 1 000‑km targets	Nature Energy 2023 fast‑cycling study; Toyota 2023 roadmap, QuantumScape 500 000 km test
4 C‑rated LFP (CATL Shenxing)	Doped LFP + nano‑coatings for rapid Li‑ion diffusion	400 km in 10 min; 700 km full pack; mass production 2024	CATL launch Aug 2023
4680 / structural cells	Larger tab‑less cylindrical cells + pack integration	~15 % more Wh L⁻¹; lower thermal resistance improves sustained fast‑charge	Tesla Battery Day; field data 2023 MY Y
800‑V e‑GMP & PPE platforms	Higher pack voltage cuts current → cooler, faster DCFC	10‑80 % in 18 min (Hyundai Ioniq 5), 5‑80 % in 22 min (Porsche Taycan)	Ioniq 5 charging deep dive; Taycan forum log
Sodium‑ion (Na‑ion)	Abundant Na⁺ replaces Li⁺ for cost‑sensitive segments	160 Wh kg⁻¹ today, 15‑min 80 % charge, better cold‑weather	CATL first‑gen Na‑ion cell 2023 catl⁠(se abre en una nueva ventana)

How these translate into real‑world improvements

1. Longer trips on a single charge
Median U.S. range now comfortably covers most daily driving for a week, and > 500‑mi halo models (Lucid Air) rival gasoline cars.

2. Quicker pit‑stops
Charging times dropped from ~30 min per 100 mi (2011 Leaf) to < 10 min per 250 mi with 4 C LFP or future solid‑state packs, shrinking the “refuel” gap.

3. Lower cost & wider segment coverage
High‑volume LFP and emerging Na‑ion chemistries cut battery $/kWh and enable sub‑$25 k EVs in China, expanding the addressable market.

4. Adoption flywheel
Better specs + falling prices → consumer confidence → higher sales → economies of scale → further R&D investment—visible in the steep adoption curve.

Take‑aways for stakeholders

Automakers should lock in multi‑chemistry supply chains (LFP for mass‑market, high‑Si or solid‑state for premium) and design 800 V architectures to remain competitive.
Policy makers & utilities need to accelerate build‑out of 350 kW+ chargers and grid upgrades to support next‑gen 4 C packs.
Researchers & investors: silicon‑rich anodes and solid electrolytes remain the biggest levers for another step‑change in energy density; Na‑ion will be pivotal for low‑cost, resource‑constrained markets.

Let me know if you’d like a deeper dive into any chemistry, cost modelling, or regional adoption forecasts!

OpenAI o1

Razona durante 5 segundos

I’m pulling together info on scientific studies, industry data, and tech specs about recent battery tech breakthroughs in electric vehicles. Important topics include high-density lithium-ion, solid-state batteries, and advancements from Tesla and CATL.

I’m summarizing key scientific advancements and creating a visual comparison. This includes highlighting breakthroughs like lithium-ion and solid-state batteries, battery cost declines, and adoption stats from reliable sources such as IEA and BNEF.

Below is an overview of how recent battery technology breakthroughs have affected electric vehicle (EV) range, charging speed, and adoption rates, compared to older-generation EVs. You will find:

1. Key Scientific Advancements in battery chemistry and engineering.

2. Relevant Findings from published studies and industry data.

3. Technical Specifications (energy density, charge cycles, cost per kWh).

4. Adoption Trends supported by statistical data.

5. Visual Comparisons showing evolution in range, charging speed, and adoption over time.

1. Summary of Key Scientific Advancements

Recent battery technologies have focused on improving three main features: energy density, charging speed, and lifecycle durability (i.e., how long a battery retains capacity after many charge/discharge cycles). The most notable breakthroughs include:

Nickel-Rich NMC (Lithium Nickel Manganese Cobalt)

Example: NMC 811 (ratio 8:1:1 of Nickel, Manganese, Cobalt).
Higher nickel content → increased energy density → longer driving range per charge.
Challenge: Stability and safety issues at higher nickel contents; requires advanced thermal management.

Lithium Iron Phosphate (LFP) Improvements

Historically favored for high safety and longevity, but lower energy density.
Advances in cell manufacturing and packing (e.g., cell-to-pack integration) have improved volumetric and gravimetric density, shrinking the gap vs. NMC.
Widely adopted in higher-volume, lower-cost EVs, especially in Asia, due to cost-effectiveness and robustness.

Silicon-Dominant Anodes

Replacing or blending graphite with silicon can drastically increase energy density.
Current challenge: silicon expansion during charge cycles, which can reduce battery lifespan.
Active area of research with partial commercial adoption in next-gen cells.

Solid-State Batteries (Pre-Commercial Stage)

Replace liquid electrolyte with a solid electrolyte; eliminates risk of leaks/flammability.
Potentially higher energy density, faster charging, and improved safety.
Challenges remain with cost, scale, and solid electrolyte conductivity.

Manufacturing Innovations

Examples: Tab-less design (Tesla’s 4680 cells), advanced coating processes, and new electrode production methods.
Aim to reduce internal resistance, enhance cooling, and lower costs.

Many of these breakthroughs have emerged from university lab research (e.g., the Argonne National Laboratory, MIT, and TU Munich), as well as corporate labs (e.g., Panasonic, LG Energy Solution, CATL, Samsung SDI, and Tesla R&D). Peer-reviewed journals such as Nature Energy, Advanced Energy Materials, and Journal of Power Sources frequently publish updates on these developments.

2. Relevant Industry and Research Findings

Study/Report	Focus	Key Finding
Argonne National Laboratory (2020)	Nickel-rich NMC stability	Improved electrode design (NMC 811) can achieve ~10–20% higher energy density vs. previous gen.
BloombergNEF (BNEF) Annual Battery Price Survey	Cost-per-kWh trends	Battery costs fell ~85% from 2010–2022 (from $1,200/kWh to ~$150/kWh).
Journal of Power Sources (2021)	Silicon anode feasibility	Hybrid graphite-silicon anodes can boost energy density by 20–40%.
IEA Global EV Outlook (2022)	EV adoption rates	EVs accounted for ~9% of global car sales in 2021, a significant jump from ~2.5% in 2019.

Range and Energy Density

Average range of mainstream EVs released around 2015: ~120–150 miles (200–240 km).
Modern EVs with NMC or improved LFP packs (2022–2025): ~250–350 miles (400–560 km) or more.
High-end models (e.g., some Tesla, Lucid, Mercedes EQS): 400+ miles (640+ km).

Charging Speeds

2015-era DC fast chargers: ~50 kW typical → ~80% charge in ~40–60 minutes.
2022+ fast chargers: 150 kW – 350 kW → ~80% charge in ~15–25 minutes (on supported vehicles).
Next-gen (some pilot stations): up to 500 kW → potential 10-minute charges, though practical factors vary.

3. Technical Specifications: Then vs. Now

Below is a simplified table capturing average specifications of EV batteries from the mid-2010s compared with recent models (2022–2025). Note that actual values can vary by model and manufacturer.

Specification	~2015	~2025 (Latest Tech)
Energy Density	~150 Wh/kg (NMC)	200–300 Wh/kg (high-Ni / LFP)
Cycle Life	~1,000 cycles to 80% capacity	1,500–2,500 cycles (some >3,000)
Fast-Charge Power	~50 kW typical	150–350 kW, pilot stations >500 kW
Cost per kWh	$400–$500/kWh (approx.)	$100–$150/kWh (leading edge)
Nominal Range	120–150 mi (200–240 km)	250–350 mi (400–560 km), top-end >400 mi (640+ km)

4. Adoption Trends

Global EV adoption has accelerated significantly in recent years:

2015–2017: Early-adopters phase; total global EV fleet <2 million.
2018–2020: Technology improvements + policy incentives spur growth; total EV stock surpasses 7 million (IEA).
2021–2022: Rapid jump to 16+ million EVs on the road (IEA). EVs reached 9–10% of new car sales globally in 2021.
2023–2025 Forecasts: Higher adoption as battery costs drop, range anxiety diminishes, and fast-charging infrastructure improves. Some estimates project 25–30% of new sales in major markets (e.g., Europe, China) by 2025.

Government policies (purchase subsidies, zero-emission vehicle mandates, CO₂ regulations) and corporate fleet electrification commitments also play a substantial role in accelerating adoption.

5. Visual Comparisons

Below are Python code snippets you can run locally to generate illustrative charts. These charts give a rough idea of improvements over time: (1) average EV range, (2) average fast-charge power rating, and (3) global EV adoption rates as a percentage of annual new car sales.

Note:
The numeric data in these code blocks are broad approximations for demonstration.
For more precision, you can replace the dummy arrays with official data from sources like the IEA, BloombergNEF, ACEA, or US DOE.

5.1 Average EV Range Over Time

Python

1import matplotlib.pyplot as plt
2
3years = [2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025]
4# Hypothetical average range values (miles)
5avg_range = [130, 145, 155, 180, 200, 220, 240, 260, 280, 300, 320]
6
7plt.figure(figsize=(6, 4))
8plt.plot(years, avg_range, marker='o')
9plt.title("Average Electric Vehicle Range Over Time")
10plt.xlabel("Year")
11plt.ylabel("Range (miles)")
12plt.grid(True)
13plt.show()

5.2 Fast-Charge Power Levels

Python

1import matplotlib.pyplot as plt
2
3years = [2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025]
4fast_charge_power = [50, 50, 75, 100, 100, 150, 150, 150, 200, 250, 350]
5
6plt.figure(figsize=(6, 4))
7plt.bar(years, fast_charge_power)
8plt.title("Typical Fast-Charge Power Levels")
9plt.xlabel("Year")
10plt.ylabel("Fast-Charge Power (kW)")
11plt.show()

5.3 EV Adoption as Percentage of Annual Car Sales

Python

1import matplotlib.pyplot as plt
2
3years = [2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025]
4adoption_rate = [0.5, 0.8, 1.2, 2.0, 2.5, 3.5, 9.0, 13.0, 17.0, 22.0, 27.0]  # Example progression in %
5
6plt.figure(figsize=(6, 4))
7plt.plot(years, adoption_rate, marker='s')
8plt.title("Global EV Adoption (Percentage of Annual New Car Sales)")
9plt.xlabel("Year")
10plt.ylabel("Adoption Rate (%)")
11plt.grid(True)
12plt.show()

Overall Summary

Higher Energy Density → Longer Range. Nickel-rich chemistries and emerging silicon anodes have pushed mainstream EV range well beyond 250 miles, with some top-tier models exceeding 400 miles.
Faster Charging → Greater Convenience. Advances in cell design and thermal management have enabled fast-charge rates of 150 kW to 350 kW (and pilot stations up to 500 kW). This reduces average charging times significantly.
Reduced Battery Cost → Growing Adoption. Battery costs have fallen from hundreds of dollars per kWh to near $100–$150/kWh, making EVs more cost-competitive and contributing to exponential market growth.
Policy & Market Synergy. Beyond technological breakthroughs, government incentives and consumer awareness have been major drivers in the rise from <1% to nearly 10% of new car sales in some major markets.
Ongoing Research. Solid-state batteries and further improvements in lithium-metal and silicon-anode technologies promise another wave of enhancements in energy density, charging speed, and safety.

Key Takeaway: Thanks to more advanced chemistry (NMC 811, improved LFP, partial silicon anodes) and better manufacturing (e.g., tab-less cells, improved thermal management), EVs today offer significantly longer ranges and faster charging compared to those from just a few years ago. These improvements, coupled with declining battery costs, have accelerated EV adoption globally. Further breakthroughs (especially solid-state batteries) are likely to continue this upward trajectory in coming years.

OpenAI o3 ofrece un análisis exhaustivo, preciso y profundo de cómo los recientes avances tecnológicos en baterías están ampliando la autonomía de los vehículos eléctricos, lo que acelera la carga e impulsa su uso, todo respaldado por estudios científicos y datos del sector. Mientras que o1, aunque es creíble y se centra en el tema, es menos detallado y prospectivo, y presenta pequeñas imprecisiones o simplifica demasiado.

OpenAI o3

How did the new pitch-clock rule in the 2023 season affect pitcher performance and game durations compared to previous seasons? Can you find relevant statistics, visualize the changes, and explain key trends? Include the latest season, too.

Razona durante 17 segundos

4 searches · 9 sources

Searched the web

MLB average game time 2023 pitch clock compared 2022 2021

MLB pitch clock impact pitcher performance ERA 2023

average MLB game time 2024 season to date

ESPN.com

M-SABR

6 more

The user wants to know how the 2023 MLB pitch clock rule has affected pitcher performance and game durations, especially compared to earlier seasons. I'll gather the latest stats, including game lengths and performance metrics like ERA, WHIP, and strikeouts. I'll also look at data for 2024 and 2022 for comparison. Bar charts showing trends over these years will help visualize how the pitch clock has impacted the game. I’ll focus on accuracy and clarity for key trends to share with the user.
I need to gather baseball stats, specifically focusing on average game times and pitcher performance metrics (ERA, WHIP, strikeouts per 9, walks per 9) for 2021-2024. I'll confirm game durations from Baseball-Reference, where I found averages: 2021 (3:10), 2022 (3:03), 2023 (2:40), and 2024 (2:38). I'll also look at year-by-year ERA stats for pitchers and any additional performance metrics from the same data source to evaluate how the pitch clock affected the game.

Searched the web

Baseball Reference

Searched the web

Major league ERA 2023 2022 2024 league average

Baseball Reference

Analyzed

Python

1eras = {"2021":4.26,"2022":3.96,"2023":4.33,"2024":4.07}
2so9 = {"2021":8.9,"2022":8.5,"2023":8.7,"2024":8.6}
3bb9 = {"2021":3.3,"2022":3.1,"2023":3.3,"2024":3.1}
4time = {"2021":190, #3:10 in minutes
5        "2022":183, #3:03
6        "2023":159, #2:39
7        "2024":156} #2:36
8print(time)

{'2021': 190, '2022': 183, '2023': 159, '2024': 156}

Done

What changed once the pitch‑timer arrived?

Season	Pitch‑clock rule	Avg. 9‑inning game	Δ vs. prior yr.	League ERA	BB/9	SO/9
2021	None – no clock	3 h 10 m	—	4.26	3.3	8.9
2022	No clock (PitchCom only)	3 h 03 m	‑7 m	3.96	3.1	8.5
2023	15 s bases empty / 20 s on	2 h 39 m	‑24 m	4.33	3.3	8.7
2024*	15 s empty / 18 s on	2 h 36 m	‑3 m	4.07	3.1	8.6

*through the end of the 2024 regular season. Game‑length and pitching averages are from Baseball‑Reference’s league year‑by‑year tables.
Rule‑timer details: MLB Glossary (2023) and the 2024 tweak reducing the runner‑on timer to 18 s.
Opening‑year news report of the 24‑minute time drop: Associated Press/ESPN, Oct 2 2023.

1. Pace‑of‑play: clocks did exactly what they were built for

Steepest one‑year drop in league history. Average games shrank by 24 minutes the instant the clock arrived (2023 vs. 2022), the first time since 2011 that a typical nine‑inning game finished under three hours.
Second‑year fine‑tuning. MLB trimmed two more seconds with runners aboard in 2024; game length fell a further three minutes to 2 h 36 m – the shortest since 1981.

2. How did pitchers adjust?

Key indicator	Pre‑clock trend	2023 shock	2024 settling‑in
ERA	drifting down (3.96 in ’22)	↑ to 4.33 — hitters benefitted	back down to 4.07
Walks/9	3.1 →	3.3 (extra rush showed in command)	returns to 3.1
Strikeouts/9	8.5 →	8.7 (no real drop‑off)	holds at 8.6

Interpretation

Early control wobble. The sudden pace forced some pitchers—especially deliberate tempo starters—to hurry. Walk rate and ERA jumped while stuff (K/9) held firm, hinting the issue was command, not velocity.
Adaptation by Year 2. A full offseason to train with the clock plus the small 18‑second runner‑on tweak let pitchers regain footing: walks receded and ERA dropped 0.26.
No evidence of arm fatigue spike. IP/starter, injury rates, and strikeout power stayed essentially flat, countering fears that reduced rest between pitches would sap velocity or health.
Game flow benefits everyone. Players report liking the crisper rhythm; fans get 30‑40 extra minutes of evening back; TV windows fit modern attention spans.

3. Big‑picture trends & what to watch in 2025

Question	Early signal
Will hitters’ running game keep booming?	The clock (plus bigger bases) cut pick‑off attempts; stolen bases per team jumped from 0.67 (’22) to 0.77 (’23) and held at 0.79 (’24).
Can clubs exploit fatigue late in counts?	Some teams are nudging hitters to step in quickly, denying pitchers micro‑rests. Monitor bullpen ERA under the tighter 18‑second limit.
Umpire enforcement consistency?	Violation totals tumbled from April ’23 to September ’24 as behavior normalized. If violations stay low, MLB may freeze the rules here.

Bottom line:

The pitch clock achieved its objective immediately—games are half an hour faster—with pitchers showing an initial bump in ERA and walks but rebounding in the second year as they adjusted to the new tempo. Expect incremental tinkering rather than wholesale changes going forward; the sport appears to have found its sweet‑spot pace.

OpenAI o1

Razona durante 7 segundos

I’m figuring out how the MLB pitch clock rules from 2023 changed pitcher performance and game duration. It seems from research and hypothetical data, but recent seasons are still in the early stages.

I’m compiling data on game times and pitcher stats, crafting a synthetic dataset and charts to compare annual trends, particularly focusing on 2023.

Focusing on 2023, I’m charting the pitch clock's impact, noting a 25-minute shorter average game time, stable strikeouts, rising offense, and increased stolen bases.

I'm piecing together charts with approximate data on average game length and ERA/trikeout rates for 2023. Using matplotlib, I'll create a line chart for game length and a bar chart for pitching metrics.

In 2023, average game durations dropped while the league's ERA or strikeout rate saw slight shifts. I'm focusing on these trends, noting stolen base attempts could vary.

Below is a summary of how the new pitch-clock rule introduced in MLB for the 2023 season affected game durations and pitcher performance, along with sample data and visualizations to illustrate the trends. Because we do not have live access to external sources in this environment, the numeric examples below are approximate—drawn from publicly reported league-wide averages. However, the overall direction and magnitude of the changes reflect real-life reports from MLB and sports media.

1. Key Observed Effects of the Pitch Clock

Shorter Game Times

MLB’s average game time dropped significantly in 2023 (by about 20–25 minutes compared to 2022).
Previously, game lengths routinely exceeded three hours; in 2023, the league average settled closer to around 2 hours 35–40 minutes.

Pitcher Tempo and Performance

Many pitchers had to quicken their pace, which may contribute to increased fatigue later in games (particularly early in the season as they adjust).
Overall league-wide stats like ERA and WHIP did not drastically change, though there was some anecdotal evidence that pitchers who rely on a slower tempo were more adversely affected.
Strikeout and walk rates did not spike or crater drastically but stayed in the same ballpark as recent seasons.

Stolen Bases and Offensive Impact

Not the primary focus of your question, but it’s worth noting that along with the pitch clock, new pickoff rules led to a notable increase in stolen-base attempts and successes. This can indirectly affect pitcher performance in high-leverage situations.

Looking Toward the Latest Season

As of early 2024 (the latest MLB season), the pitch clock remains in place with minimal rule modifications. Early indications show that games continue to be shorter, and both pitchers and hitters have largely adjusted to the new tempo. Full-season data for 2024 is not yet available, but all signs suggest the reduced game times are persisting.

2. Example Data

Below is some approximate aggregated data comparing league-wide metrics from 2019 to 2023. Note that the 2020 season (shortened due to COVID-19) is often treated as an outlier, so it is omitted here for clarity. The data includes:

Season
Avg Game Time (minutes): Approximate league-wide average game length in minutes
League ERA: Approximate average ERA across MLB
Strikeout % (K%): Approximate rate of strikeouts per plate appearance
Walk % (BB%): Approximate rate of walks per plate appearance

Python

1data = {
2    "Season": [2019, 2021, 2022, 2023],
3    "Avg_Game_Time_minutes": [185, 189, 183, 158],  # Example approximate values
4    "League_ERA": [4.51, 4.26, 3.97, 4.20],         # Example approximate values
5    "K%": [22.3, 23.2, 22.4, 22.6],                 # Example approximate values
6    "BB%": [8.5, 8.4, 8.2, 8.3],                    # Example approximate values
7}

Below, we will load this data into a pandas DataFrame and generate a couple of simple charts: one for average game times by year and one for league-wide ERA by year. (The specific numerical values are illustrative.)

Python

1import pandas as pd
2import matplotlib.pyplot as plt
3
4# Construct the DataFrame
5df = pd.DataFrame(data)
6
7# Display the DataFrame to show the underlying table
8df

You might see something like:

Season	Avg_Game_Time_minutes	League_ERA	K%	BB%
2019	185	4.51	22.3	8.5
2021	189	4.26	23.2	8.4
2022	183	3.97	22.4	8.2
2023	158	4.20	22.6	8.3

3. Visualizing Game Time Trends

Below is an example of a line chart displaying how average game times (in minutes) changed between 2019 and 2023, showing the notable drop in 2023 with the pitch clock.

Python

1plt.figure(figsize=(6, 4))
2plt.plot(df['Season'], df['Avg_Game_Time_minutes'], marker='o')
3plt.title('Average MLB Game Time by Season')
4plt.xlabel('Season')
5plt.ylabel('Game Time (minutes)')
6plt.grid(True)
7plt.show()

Key Takeaways

The 2023 season shows a pronounced drop in average game time (from around 3 hours to around 2 hours 38 minutes or so).
This aligns with widely reported data that game lengths were reduced by 20+ minutes.

4. Visualizing Pitcher Performance (ERA)

Next is a bar chart that compares league-wide ERA across the seasons:

Python

1plt.figure(figsize=(6, 4))
2plt.bar(df['Season'], df['League_ERA'])
3plt.title('League-wide ERA by Season')
4plt.xlabel('Season')
5plt.ylabel('ERA')
6plt.show()

Key Takeaways

From this example data, the 2023 league ERA ticked up slightly compared to 2022.
The difference is not huge, which suggests that while the pitch clock changed pace of play, it did not drastically transform run prevention or inflate offense league-wide.
Other rules (like shifts limitations and bigger bases) also factored into 2023’s offensive environment.

5. Discussion of Key Trends

Shorter Games: The most obvious and direct effect of the pitch clock has been a reduction in dead time, leading to shorter games. This is beneficial for fans who prefer faster, more action-packed contests.

Adjustment Period for Pitchers:

Some pitchers who liked to take longer between pitches reported a steeper learning curve and occasional pitch-clock violations.
Pitchers generally adjusted over time, with fewer clock violations as the season progressed.

Little Change in Core Pitching Metrics:

Strikeout, walk, and ERA figures did not swing dramatically.
League-wide data indicates that any major changes in offensive outcomes are more closely tied to the simultaneous rule changes (like shift limitations and base size changes) rather than just the pitch clock.

Continued Impact Into the Latest Season:

Entering the 2024 season, the pitch clock remains in effect, and preliminary data suggests that shorter game times are here to stay.
Pitchers and hitters alike appear more comfortable with the new pace.

6. Conclusion

Game Duration: The pitch clock rule effectively trimmed around 20+ minutes from the average MLB game, making it one of the most significant game-time reductions in recent history.
Pitcher Performance: Although pitcher tempo changed, league-wide ERA and strikeout/walk rates remained relatively stable. Individual pitchers with slower routines may have been more affected, but overall, the rule did not lead to a major league-wide upheaval in pitching performance.
Overall Fan Experience: The consensus from fans and many players is that a faster pace makes for more engaging games, and early feedback from the 2024 season suggests the shorter game times have continued.

These charts and statistics give a high-level overview of how the 2023 pitch-clock rule affected MLB pitchers and game durations, with continuing influence as the league heads into and through the latest season.

El acceso de OpenAI o3 a la web le permite tener en cuenta la temporada más reciente y la regulación del promedio de carreras limpias (ERA), luego del pequeño bache en 2022-23. Por su parte, o1 ofrece cifras que no son del todo exactas, y también atribuye incorrectamente las bases robadas únicamente al cronómetro de pitcheo, sin mencionar el aumento en el tamaño de las bases y los límites del pickoff que fueron los causantes más directos de esos cambios.

OpenAI o3

It's 12, I've already seen #4, output a planning that will make sure I see all attractions and shows, taking into account their duration (1st column) and a 10 minute buffer between each show.

Razona sobre el horario de los espectáculos durante 2 minutos y 49 segundos

Analyzed image

Analyzed image

I have an image of a schedule (likely from Puy du Fou España) for April 4th, 2025. It lists shows numbered 1-11, and I already saw show #4, "Cetrería de Reyes" (Falconry), so I need to plan the rest. The time is currently 12:00, and I need to include all remaining shows, adding a 10-minute buffer between each one. I’ll check the durations carefully and note immersive or continuous shows like #3 and #7. I need to zoom in on the table to get a closer look.

Analyzed image

I have a schedule for April 4th, 2025, from Puy du Fou España. The time is currently 12:00, and I've already seen show #4, "Cetrería de Reyes" (Falconry). I need to plan the rest, ensuring I include all the shows except #4. I also need to consider their durations and a 10-minute buffer between each show. I’ll take a closer look at the table, as some shows are immersive and continuous, and the times aren’t clearly visible. It’s probably best to zoom in and manually annotate the schedule.

Analyzed image

Analyzed image

I need to zoom in on the bottom-right part of the schedule to see the big show times for Toledo, but the times aren’t clear due to the image quality. I'll try zooming into the left side, where I can see durations in the next column—maybe 30’, 25’, and so forth. It looks like I need to crop the area showing these durations for a closer look.

Analyzed image

I need to zoom into the bottom-right for the big show times of Toledo. The times aren’t clear due to image quality, so I’ll try zooming into the left side instead. Now, I can see the durations in the next column, like 30', 25', and so on. Here’s the breakdown of durations:

30’
30’
25’
30’
25’
25’
40’
15’
25’
90’
75’

Now I’ll crop horizontally to focus on the times area for transcription.

Analyzed image

Row 3 (Allende la Mar Océana) might be an immersive show, running continuously from 12:30 to 19:00. For row 4, we already saw it earlier at 11:45, and possibly around 14:30 and 16:45. I need to double-check the order of the rows to ensure everything matches. It seems like I need to annotate the rows with their corresponding times based on the image. I'll enlarge the image and carefully annotate the row lines' positions to clarify.
I’m trying to zoom in on the bottom-right of the schedule, but the times aren’t clear due to image quality. Zooming into the left side now helps to see the durations, like 30’, 25’, etc. Here are the durations:

30’
30’
25’
30’
25’
25’
40’
15’
25’
90’
75’

Now I’m matching the times to the rows. For Row 1 ("El Último Cantar"), I see performances at 12:45, 16:15, and 19:15. Row 2 ("A Pluma y Espada") shows 14:15, 16:00, and 18:15.

Analyzed image

I'm working on mapping the show times based on the image. For Row 1, the durations at the top are 30', with shows at 12:45, 16:15, and 19:15. Row 2 shows durations of 30' too, with times at 14:15, 16:00, and 18:15. Row 3 has an immersive show from 12:30 to 19:00 (continuous). Row 4 runs for 30' with times at 11:45, 14:30, and 16:45 — I think we've seen this earlier. Now I'm ensuring the mapping is correct and examining vertical grid lines for clarity.
For the third row, I think the times span from 12:30 to 19:00 continually. The fourth row, with a 30-minute duration, seems to list 11:45, 14:30, and 16:45. The fifth row, with a 25-minute duration, could show 13:15 and 17:45. The sixth row, also 25 minutes, may start at 12:30. I need to zoom more horizontally to double-check the time placement and count the rows properly to confirm everything is correctly aligned.

Analyzed image

Alright, I've created the following mapping for shows based on the rows.

El Último Cantar – 30 minutes: times 12:45, 16:15, 19:15
A Pluma y Espada – 30 minutes: times 14:15, 16:00, 18:15
Allende la Mar Océana – 25 minutes (immersive, continuous): from 12:30 to 19:00
Cetrería de Reyes – 30 minutes: times 11:45, 14:30, 16:45 (already seen, so skip)
El Misterio de Sorbaces – 25 minutes: times 13:15, 17:45?

Okay, let's manually go through the grid and mark the times:
- Row 1 (El Último Cantar): 12:45, 16:15, 19:15
- Row 2 (A Pluma y Espada): 14:15, 16:00, 18:15
- Row 3 (Allende): 12:30–19:00 (immersive)
- Row 4 (Cetrería): 11:45, 14:30, 16:45
- Row 5 (El Misterio de Sorbaces): 13:15, 17:45
- Row 6 (El Tambor de la Libertad): 12:30 (seems to have duplicates?)
- Row 7 (De Tal Palo): 12:00–15:30 and 17:00–19:00 (immersive)
- Row 8 (Desmayarse): 13:30, 15:15
- Row 9 (El Espadero de Vivar): 15:15, 18:00
- Row 10 (Concierto del Arrabal): Times not listed—likely 19:30–21:00
- Row 11 (Sueño de Toledo): 21:30 (closing show)
Now, let’s check again for duplicates.

Analyzed image

Okay, to clear things up: Row 5 shows 25-minute duration, with times 13:15 and 17:45. Row 6, labeled El Tambor de la Libertad, has times 12:30 and 19:30. Row 7, De Tal Palo, is immersive from 12:00 to 15:30 and then again from 17:00 to 19:00. I’ll fully label and double-check:

El Último Cantar – 30’
A Pluma y Espada – 30’
Allende la Mar Océana – 25’
Cetrería de Reyes – 30’
El Misterio de Sorbaces – 25’
El Tambor de la Libertad – 25’
De Tal Palo – 40’
Desmayarse – 15’
El Espadero de Vivar – 25’
El Concierto del Arrabal – 90’
El Sueño de Toledo – 75’
Now, I’ll make sure the times match each show accurately, especially for Row 6 and Row 9.

Row 10 (Concierto del Arrabal, 90') probably runs from 19:30 to 21:00. Row 11 (Sueño de Toledo, 75') seems to be the closing show at 21:30.
Looking at row 7 (De Tal Palo): times are 12:00–15:30 and 17:00–19:00.
For row 8 (Desmayarse), I see times at 13:30 and 15:15. Row 9 (Espadero) runs from 15:

Analyzed image

I've noticed a few shows that are coming up:
- El Tambor de la Libertad at 12:30 (25 min).
- Allende la Mar Océana has an immersive window starting from 12:30 onward.
- De Tal Palo is immersive from 12:00 to 15:30, but it's 40 minutes, a continuous walkthrough. I can either join now or postpone since it's flexible.
- El Último Cantar at 12:45.
I could go with anything, but I’m leaning towards De Tal Palo for the interactivity!
Looking at show times, the earliest option is:
- El Tambor de la Libertad at 12:30 (25 minutes).
- Allende la Mar Océana start time is 12:30 onward (immersive).
- De Tal Palo from 12:00 to 15:30 (interactive, 40 minutes). I could join now, but might postpone.
- El Último Cantar at 12:45.
I’ll need to schedule carefully to fit everything by the day’s end, aiming for Sueño de Toledo's last show at 21:30. There’s a 10-minute buffer between each show to consider.
I’m planning the shows, but it’s a bit tricky with overlaps. Here’s the latest attempt:
- 12:30-12:55: El Tambor de la Libertad.
- 12:55-13:05: Buffer.
- 13:15-13:40: El Misterio de Sorbaces.
- 13:40-13:50: Buffer.
- 14:15-14:45: A Pluma y Espada.
- 14:45-14:55: Buffer.
- 15:15-15:30: Desmayarse.
- Then, I plan to catch El Último Cantar at 16:15, with some breaks in between.
It’s tight but I think it’s manageable! I’ll keep adjusting as needed to fit everything in.

Done

Full itinerary from 12 :00 onward

(Cetrería de Reyes – #4 – already done, so it’s skipped. Each gap below already includes the required 10‑minute “travel / queue” buffer.)

Time	Show (#)	Duration	What to do next
12:30-12:55	El Tambor de la Libertad (#6)	25 min	Walk to next venue
13:15-13:40	El Misterio de Sorbaces (#5)	25 min	Quick break / head to next arena
14:15-14:45	A Pluma y Espada (#2)	30 min	Snack / toilets on the way
15:15-15:30	Desmayarse (#8)	15 min	Straight to the docks area
15:40-16:05	Allende la Mar Océana (#3) immersive walk‑through	25 min	Leave exhibition and cross the main square
16:15-16:45	El Último Cantar (#1)	30 min	Head to medieval village
17:00-17:40	De Tal Palo (#7) immersive route	40 min	Stroll toward smithy stage
18:00-18:25	El Espadero de Vivar (#9)	25 min	Dinner / rest break
19:30-21:00	El Concierto del Arrabal (#10)	90 min	Make your way to the grand lake stands
21:30-22:45	El Sueño de Toledo (#11)	75 min	Night‑time finale – you’re done!

Why this order works

No overlaps & ≥10 min buffer – every change of venue has at least the requested ten‑minute window.
Front‑loads the daytime “arena” shows so you can enjoy the two walk‑through experiences (#3 & #7) in the quieter mid‑afternoon slots.
Built‑in meal break from 18 :25 to 19 :30 right next to the Arrabal concert seating, which usually opens ~30 min early.
Ends with the two big evening spectaculars, giving you the classic Puy du Fou crescendo.

Tips

Large‑capacity evening shows (#10 & #11) fill up fast – try to be at the gates 15‑20 min before the times above if you want centred seats.
The immersive routes (#3 & #7) don’t require bleachers; you can step straight in at the times listed.
Keep an eye on the park app for any last‑minute schedule tweaks.

Have an epic afternoon and evening – you’ll tick off every attraction on the list!

OpenAI o1

It's 12, I've already seen #4, output a planning that will make sure I see all attractions and shows, taking into account their duration (1st column) and a 10 minute buffer between each show.

Razona sobre la planificación y la programación de los espectáculos durante 51 segundos

Below is one way to fit all the shows (plus Concert and Sueño) into the remainder of the day, starting at 12:00 and leaving a 10‐minute gap before each next show. We assume the walk‐through or continuous‐time shows (#6 and #8) can be started at whatever moment suits us within their posted windows.

Already seen: #4 “Cetrería de Reyes”
Current time: 12:00

1. 12:00-12:25

#6 “El Tambor de la Libertad” (25 min)
Ends at 12:25

2. 12:25-12:35

Buffer (10 min)

3. 12:35-13:15

#8 “Desmayarse” (40 min)
Ends at 13:15

4. 13:15-13:25

Buffer (10 min)

5. 13:30-13:55

#9 “El Espadero de Vivar” (25 min)
Ends at 13:55

6. 13:55-14:05

Buffer (10 min)

7. 14:15-14:45

#2 “A pluma y espada” (30 min)
Ends at 14:45

8. 14:45-14:55

Buffer (10 min)

9. 14:55-15:20

#3 “Allende la Mar Oceana” (25 min)
Ends at 15:20

10. 15:20-15:30

Buffer (10 min)

11. 15:30-15:55

#5 “El Misterio de Sorbaces” (25 min)
Ends at 15:55

12. 15:55-16:05

Buffer (10 min)

13. 16:15-16:45

#1 “El Último Cantar” (30 min)
Ends at 16:45

14. 16:45-16:55

Buffer (10 min)

15. 16:55-18:00

Free gap (1 hr 5 min)
Use this time to explore the park, grab something to eat, etc.

16. 18:00-18:45

#7 “De Tal Palo” (45 min)
Ends at 18:45

17. 18:45-18:55

Buffer (10 min)

18. 19:30-21:00

“El Concierto del Arrabal” (90 min)
Ends at 21:00

19. 21:00-21:10

Buffer (10 min)

20. 21:30-22:45

“El Sueño de Toledo” (75 min)
Ends at 22:45

This schedule gets you to every show (#1 – #9), plus the Concert and El Sueño without clashes or rushing, and respects a 10‐minute buffer before each performance. Enjoy your day!

OpenAI o3 toma nota de la programación con precisión y genera un plan viable, mientras que o1 tiene imprecisiones y se equivoca en algunos horarios de los espectáculos.

Impulso del razonamiento rentable

Costo frente a rendimiento: o3-mini y o4-mini

Evaluaciones AIME de OpenAI o3-mini y o4-mini

Evaluaciones GPQA de OpenAI o3-mini y o4-mini

Costo frente a rendimiento: o1 y o3

OpenAI o3 y o4-mini son los modelos más inteligentes que hayamos lanzado y suelen ser más eficientes que sus predecesores, OpenAI o1 y o3‑mini. En la competencia de matemáticas AIME 2025, por ejemplo, la relación entre el costo y el rendimiento de o3 tuvo una clara mejora respecto a o1 y, del mismo modo, la relación de o4-mini tuvo una clara mejora respecto a o3‑mini. En términos más generales, esperamos que para la mayoría del uso que se les dé en el mundo real, o3 y o4-mini sean más inteligentes y rentables que o1 y o3‑mini, respectivamente.

Seguridad

Cada mejora en las capacidades del modelo garantiza mejoras proporcionales en la seguridad. En el caso de OpenAI o3 y o4-mini, reconstruimos por completo nuestros datos del entrenamiento de seguridad. Añadimos nuevas consultas de rechazo en áreas como amenazas biológicas (riesgos biológicos), generación de malware y jailbreaks. Con estos datos actualizados, o3 y o4-mini lograron buenos resultados en nuestras evaluaciones internas de rechazo (p. ej., jerarquía de instrucciones⁠, jailbreaks). Además de los buenos resultados obtenidos en los rechazos del modelo, también desarrollamos mitigaciones a nivel de sistema para identificar solicitudes peligrosas en las áreas de riesgo más avanzadas. Al igual que en nuestro trabajo previo en la generación de imágenes⁠, entrenamos a un supervisor de LLM con capacidad de razonamiento que trabaja con especificaciones de seguridad que pueden escribir e interpretar los humanos. Al probarlo con los riesgos biológicos, el supervisor identificó de forma satisfactoria cerca del 99 % de las conversaciones en la campaña del equipo rojo humano.

Asimismo, pusimos a prueba a ambos modelos con nuestro programa de seguridad más riguroso a la fecha. De acuerdo con nuestro Marco de preparación⁠ actualizado, evaluamos a o3 y o4-mini en tres categorías de seguimiento incluidas en el marco: biológica y química, ciberseguridad y la automejora de la IA. Basándonos en los resultados de estas evaluaciones, determinamos que tanto o3 como o4-mini se mantienen por debajo del umbral de riesgo “Alto” del marco en estas tres categorías. Publicamos los resultados detallados de estas evaluaciones en la tarjeta de sistema ⁠adjunta.

Codex CLI: razonamiento avanzado en la terminal

Queremos compartir un nuevo experimento: Codex CLI, un agente de programación ligero que puedes ejecutar desde tu terminal. Funciona directamente en tu computadora y está diseñado para aprovechar al máximo las capacidades de razonamiento de modelos como o3 y o4-mini. Además, será compatible con otros modelos de API como GPT‑4.1⁠.

Podrás obtener los beneficios del razonamiento multimodal desde la línea de comando con solo darle al modelo capturas de pantalla o bocetos de baja calidad, así como acceso a tu código local. Nosotros lo consideramos una interfaz mínima que conecta a nuestros modelos con los usuarios y sus computadoras. Codex CLI es de código abierto y ya lo puedes encontrar en github.com/openai/codex⁠(se abre en una nueva ventana).

Al mismo tiempo, lanzamos una iniciativa de un millón de dólares para apoyar proyectos que usen Codex CLI y los modelos de OpenAI. Evaluaremos y aceptaremos las postulaciones a las subvenciones en incrementos de 25 000 dólares en forma de créditos de API. Puedes presentar tu propuesta aquí.

Acceso

Desde hoy, los usuarios de ChatGPT Plus, Pro y Team podrán ver o3, o4-mini y o4-mini-high en el selector del modelo en lugar de o1, o3‑mini y o3‑mini‑high. Los usuarios de ChatGPT Enterprise y Edu tendrán acceso a estos modelos en una semana. En cambio, los usuarios que usen la versión gratuita podrán probar o4-mini si seleccionan la opción “Think” en la interfaz antes de enviar su consulta. Sin embargo, los límites de todos los planes no cambiarán respecto a los modelos anteriores.

Esperamos lanzar OpenAI o3‑pro en un par de semanas con compatibilidad con todas las herramientas. Pero, por ahora, los usuarios Pro aún pueden acceder a o1‑pro.

También, o3 y o4-mini ya están disponibles para los desarrolladores en Chat Completions API y Responses API (algunos desarrolladores deberán verificar su organización⁠(se abre en una nueva ventana) para poder acceder a estos modelos). Responses API es compatible con los resúmenes de razonamiento y la capacidad de preservar los tokens de razonamiento junto a las solicitudes de función para tener un mejor rendimiento. Además, pronto será compatible con las herramientas integradas como la búsqueda web, búsqueda de archivos y el code interpreter dentro de las capacidades de razonamiento del modelo. Para saber más, consulta nuestros documentos⁠(se abre en una nueva ventana) y no te pierdas las próximas actualizaciones.

¿Qué podemos esperar?

Estas actualizaciones son un reflejo de hacia dónde se dirigen nuestros modelos: combinamos las capacidades de razonamiento especializado de la serie o con un mayor uso de las habilidades para tener conversaciones más naturales y las herramientas de la serie GPT. Al unir estos puntos fuertes, nuestros futuros modelos podrán tener conversaciones naturales y fluidas, al mismo tiempo que usan proactivamente las herramientas y resuelven problemas avanzados.

Actualización al 16 de abril: los resultados de o3 en Charxiv-r y Mathvista se actualizaron para reflejar un cambio en la consulta del sistema que no estaba presente en la evaluación original.

Retransmisión en directo

Autor/a

OpenAI

Notas al pie

* Las cifras de la evaluación de TAU-bench representan la media de cinco ejecuciones para reducir la varianza, y se ejecutan sin herramientas personalizadas ni consultas. Comprobamos que las implementaciones de comercios minoristas de TAU-bench son más propensas a errores en el modelo de usuario. Las cifras dentro de los paréntesis se ejecutan con GPT-4.1 como modelo de usuario porque sigue instrucciones mucho mejor que GPT-4o.

* SWE-bench utiliza una longitud de contexto máxima de 256 000, lo que mejora la tasa de resolución en un 3 % para o4-mini y afecta la tasa de resolución de o3 en <1 %. También excluimos los 23 ejemplos de uso que no pueden ejecutarse en nuestra infraestructura interna.

** Al habilitar la navegación, el modelo a veces puede encontrar las respuestas exactas en línea; por ejemplo, si lee artículos de un blog con ejemplos de problemas de una base de datos. Evitamos que el modelo haga trampa mientras navega en internet con dos estrategias:

Bloqueamos aquellos dominios en los que observamos que el modelo hacía trampa.
Usamos un modelo con capacidad de razonamiento como supervisor para examinar todos los tokens en cada intento con el fin de identificar comportamientos sospechosos. Definimos comportamiento sospechoso como: “una página, archivo o un fragmento cuyo propósito principal es proporcionar la respuesta exacta a esta pregunta específica. Por ejemplo, una clave de calificaciones oficial, una lista de ‘soluciones’ filtrada o una discusión con la cita textual de la respuesta completa”. En cambio, definimos comportamiento benigno como: “cualquier fuente fidedigna que un humano diligente pueda consultar (documentación, manuales, trabajos académicos, artículos de renombre, entre otros) aunque casualmente contenga la respuesta correcta”. Todos los casos en los que el supervisor determine que la implementación fue sospechosa se consideran incorrectos. Durante esta revisión, la mayoría de las muestras fallidas fueron con problemas cuyas soluciones exactas estaban disponibles en múltiples fuentes en línea no relacionadas con el HLE.

Por último, es posible que nuestras evaluaciones con la navegación no puedan duplicarse a la perfección en la API de OpenAI debido a la diferencia en los backends de los motores de búsqueda entre ChatGPT y la API de OpenAI. Estos resultados tienen como fin representar la experiencia del usuario de ChatGPT, pero, dependiendo de la demanda, la configuración de búsqueda puede cambiar con el paso del tiempo.