Function checkDeriv

test/compute-engine/calculus.test.ts:696–713

(integrandLatex: string, antiderivLatex: string)

    ce.precision = 'machine';
    try {
      const integrand = ce.parse(integrandLatex);
      const dAnti = ce.expr(['D', ce.parse(antiderivLatex), 'x']).evaluate();
      for (const xv of sample) {
        const a = dAnti.subs({ x: xv }).N().re;
        const b = integrand.subs({ x: xv }).N().re;
        if (a === null || b === null) continue;
        if (!isFinite(a) || !isFinite(b)) continue;
        expect(Math.abs(a - b)).toBeLessThan(1e-7 * (1 + Math.abs(b)));
      }
    } finally {
      ce.precision = saved;
    }
  };

  // Gaussian → error functions (completing the square selects Erf vs Erfi).
  test('∫e^(−x²) dx → (√π/2)·Erf(x)', () => {
    expect(evaluate('\\int e^{-x^2} dx')).toMatchInlineSnapshot(
      `1/2 * Erf(x) * sqrt(pi)`
    );
    checkDeriv('e^{-x^2}', '\\frac{\\sqrt{\\pi}}{2}\\mathrm{Erf}(x)');
  });