Average Error: 30.5 → 0.0
Time: 10.2s
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 r1565698 = 1.0;
        double r1565699 = x;
        double r1565700 = cos(r1565699);
        double r1565701 = r1565698 - r1565700;
        double r1565702 = sin(r1565699);
        double r1565703 = r1565701 / r1565702;
        return r1565703;
}
↓
double f(double x) {
        double r1565704 = x;
        double r1565705 = 2.0;
        double r1565706 = r1565704 / r1565705;
        double r1565707 = tan(r1565706);
        return r1565707;
}

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 2019149 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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