Average Error: 29.9 → 0.0
Time: 11.5s
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 r958170 = 1.0;
        double r958171 = x;
        double r958172 = cos(r958171);
        double r958173 = r958170 - r958172;
        double r958174 = sin(r958171);
        double r958175 = r958173 / r958174;
        return r958175;
}
↓
double f(double x) {
        double r958176 = x;
        double r958177 = 2.0;
        double r958178 = r958176 / r958177;
        double r958179 = tan(r958178);
        return r958179;
}

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 2019153 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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