Average Error: 29.7 → 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 r1643783 = 1.0;
        double r1643784 = x;
        double r1643785 = cos(r1643784);
        double r1643786 = r1643783 - r1643785;
        double r1643787 = sin(r1643784);
        double r1643788 = r1643786 / r1643787;
        return r1643788;
}
↓
double f(double x) {
        double r1643789 = x;
        double r1643790 = 2.0;
        double r1643791 = r1643789 / r1643790;
        double r1643792 = tan(r1643791);
        return r1643792;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original29.7
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 29.7

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

  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 2019139 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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