Average Error: 30.1 → 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 r2030688 = 1.0;
        double r2030689 = x;
        double r2030690 = cos(r2030689);
        double r2030691 = r2030688 - r2030690;
        double r2030692 = sin(r2030689);
        double r2030693 = r2030691 / r2030692;
        return r2030693;
}
↓
double f(double x) {
        double r2030694 = x;
        double r2030695 = 2.0;
        double r2030696 = r2030694 / r2030695;
        double r2030697 = tan(r2030696);
        return r2030697;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original30.1
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.1

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

  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 2019124 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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