Average Error: 29.8 → 0
Time: 11.2s
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 r1338759 = 1.0;
        double r1338760 = x;
        double r1338761 = cos(r1338760);
        double r1338762 = r1338759 - r1338761;
        double r1338763 = sin(r1338760);
        double r1338764 = r1338762 / r1338763;
        return r1338764;
}
↓
double f(double x) {
        double r1338765 = x;
        double r1338766 = 2.0;
        double r1338767 = r1338765 / r1338766;
        double r1338768 = tan(r1338767);
        return r1338768;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.8
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 29.8

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

  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 2019133 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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