Average Error: 30.7 → 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 r1915803 = 1.0;
        double r1915804 = x;
        double r1915805 = cos(r1915804);
        double r1915806 = r1915803 - r1915805;
        double r1915807 = sin(r1915804);
        double r1915808 = r1915806 / r1915807;
        return r1915808;
}
↓
double f(double x) {
        double r1915809 = x;
        double r1915810 = 2.0;
        double r1915811 = r1915809 / r1915810;
        double r1915812 = tan(r1915811);
        return r1915812;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.7
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.7

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

  2. Simplified0

    \[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)}\]

  3. Final simplification0

    \[\leadsto \tan \left(\frac{x}{2}\right)\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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