Average Error: 29.9 → 0.0
Time: 10.7s
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 r2532368 = 1.0;
        double r2532369 = x;
        double r2532370 = cos(r2532369);
        double r2532371 = r2532368 - r2532370;
        double r2532372 = sin(r2532369);
        double r2532373 = r2532371 / r2532372;
        return r2532373;
}
↓
double f(double x) {
        double r2532374 = x;
        double r2532375 = 2.0;
        double r2532376 = r2532374 / r2532375;
        double r2532377 = tan(r2532376);
        return r2532377;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.9
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 29.9

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

  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 2019163 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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