Average Error: 30.4 → 0
Time: 9.8s
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 r504745 = 1.0;
        double r504746 = x;
        double r504747 = cos(r504746);
        double r504748 = r504745 - r504747;
        double r504749 = sin(r504746);
        double r504750 = r504748 / r504749;
        return r504750;
}
↓
double f(double x) {
        double r504751 = x;
        double r504752 = 2.0;
        double r504753 = r504751 / r504752;
        double r504754 = tan(r504753);
        return r504754;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.4
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.4

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

  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 2019144 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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