Average Error: 30.1 → 0
Time: 10.5s
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 r1436921 = 1.0;
        double r1436922 = x;
        double r1436923 = cos(r1436922);
        double r1436924 = r1436921 - r1436923;
        double r1436925 = sin(r1436922);
        double r1436926 = r1436924 / r1436925;
        return r1436926;
}
↓
double f(double x) {
        double r1436927 = x;
        double r1436928 = 2.0;
        double r1436929 = r1436927 / r1436928;
        double r1436930 = tan(r1436929);
        return r1436930;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.1
Target0
Herbie0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.1

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

  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 2019141 +o rules:numerics
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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