Average Error: 30.5 → 0.0
Time: 11.5s
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 r756051 = 1.0;
        double r756052 = x;
        double r756053 = cos(r756052);
        double r756054 = r756051 - r756053;
        double r756055 = sin(r756052);
        double r756056 = r756054 / r756055;
        return r756056;
}
↓
double f(double x) {
        double r756057 = x;
        double r756058 = 2.0;
        double r756059 = r756057 / r756058;
        double r756060 = tan(r756059);
        return r756060;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original30.5
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.5

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

  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 2019128 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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