Average Error: 30.3 → 0.0
Time: 11.9s
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 r1769291 = 1.0;
        double r1769292 = x;
        double r1769293 = cos(r1769292);
        double r1769294 = r1769291 - r1769293;
        double r1769295 = sin(r1769292);
        double r1769296 = r1769294 / r1769295;
        return r1769296;
}
↓
double f(double x) {
        double r1769297 = x;
        double r1769298 = 2.0;
        double r1769299 = r1769297 / r1769298;
        double r1769300 = tan(r1769299);
        return r1769300;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original30.3
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.3

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

  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 2019112 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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