Average Error: 30.8 → 0.0
Time: 11.2s
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 r2769528 = 1.0;
        double r2769529 = x;
        double r2769530 = cos(r2769529);
        double r2769531 = r2769528 - r2769530;
        double r2769532 = sin(r2769529);
        double r2769533 = r2769531 / r2769532;
        return r2769533;
}
↓
double f(double x) {
        double r2769534 = x;
        double r2769535 = 2.0;
        double r2769536 = r2769534 / r2769535;
        double r2769537 = tan(r2769536);
        return r2769537;
}

Error

Bits error versus x

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Results

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Target

Original30.8
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.8

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

  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 2019158 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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