Average Error: 30.2 → 0.0
Time: 10.9s
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 r945415 = 1.0;
        double r945416 = x;
        double r945417 = cos(r945416);
        double r945418 = r945415 - r945417;
        double r945419 = sin(r945416);
        double r945420 = r945418 / r945419;
        return r945420;
}
↓
double f(double x) {
        double r945421 = x;
        double r945422 = 2.0;
        double r945423 = r945421 / r945422;
        double r945424 = tan(r945423);
        return r945424;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.2
Target0.0
Herbie0.0
\[\tan \left(\frac{x}{2}\right)\]

Derivation

  1. Initial program 30.2

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

  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 2019151 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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