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Apply numerical methods and scientific computing techniques
Passed 19 of 22 test cases with the skill, and 15 of 22 without it.
and 3 more in the full report
4 fixed15 passed either way3 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 4 test cases the skill fixed. Same model, same prompt, with and without the skill.
In a Python wrapper around scipy.integrate.solve_ivp, what specific dictionary key should store the total number of function evaluations performed by the solver?
| Checked | Without skill | With skill |
|---|---|---|
| The count of function evaluations is stored under the key 'n_evaluations'. | Missed | Passed |
The instructions your model reads when the skill loads.
A skill for applying numerical methods in scientific computing and research. Covers root finding, numerical integration, ODE solvers, optimization, interpolation, and error analysis with practical implementations in Python.
import numpy as np
def newton_method(f, df, x0: float, tol: float = 1e-10,
max_iter: int = 100) -> dict:
"""
Newton's method for finding roots of f(x) = 0.
Args:
f: Function whose root we seek
df: Derivative of f
x0: Initial guess
tol: Convergence tolerance
max_iter: Maximum iterations
"""
x = x0
history = [x]
for i in range(max_iter):
fx = f(x)
dfx = df(x)
if abs(dfx) < 1e-15:
return {"root": x, "converged": False,
"reason": "Zero derivative encountered"}
x_new = x - fx / dfx
history.append(x_new)
if abs(x_new - x) < tol:
return {
test cases passed, vs 15 / 22 without
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