Average Error: 30.8 → 0.0
Time: 10.5s
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 r806961 = 1.0;
        double r806962 = x;
        double r806963 = cos(r806962);
        double r806964 = r806961 - r806963;
        double r806965 = sin(r806962);
        double r806966 = r806964 / r806965;
        return r806966;
}
↓
double f(double x) {
        double r806967 = x;
        double r806968 = 2.0;
        double r806969 = r806967 / r806968;
        double r806970 = tan(r806969);
        return r806970;
}

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 2019142 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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