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 r5816964 = 1.0;
        double r5816965 = x;
        double r5816966 = cos(r5816965);
        double r5816967 = r5816964 - r5816966;
        double r5816968 = sin(r5816965);
        double r5816969 = r5816967 / r5816968;
        return r5816969;
}
↓
double f(double x) {
        double r5816970 = x;
        double r5816971 = 2.0;
        double r5816972 = r5816970 / r5816971;
        double r5816973 = tan(r5816972);
        return r5816973;
}

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 2019120 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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