Average Error: 30.4 → 0.0
Time: 11.1s
Precision: 64
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]
\frac{1 - \cos x}{\sin x}
↓
\tan \left(\frac{x}{2}\right)
double f(double x) {
        double r2434023 = 1.0;
        double r2434024 = x;
        double r2434025 = cos(r2434024);
        double r2434026 = r2434023 - r2434025;
        double r2434027 = sin(r2434024);
        double r2434028 = r2434026 / r2434027;
        return r2434028;
}
↓
double f(double x) {
        double r2434029 = x;
        double r2434030 = 2.0;
        double r2434031 = r2434029 / r2434030;
        double r2434032 = tan(r2434031);
        return r2434032;
}

Error

Bits error versus x

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Results

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Target

Original30.4
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.4

    \[\frac{1 - \cos x}{\sin x}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)}\]

  3. Final simplification0.0

    \[\leadsto \tan \left(\frac{x}{2}\right)\]

Reproduce

herbie shell --seed 2019132 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

  :herbie-target
  (tan (/ x 2))

  (/ (- 1 (cos x)) (sin x)))