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

↓

\[\tan \left(\frac{x}{2}\right)\]

double f(double x) {
        double r2375336 = 1.0;
        double r2375337 = x;
        double r2375338 = cos(r2375337);
        double r2375339 = r2375336 - r2375338;
        double r2375340 = sin(r2375337);
        double r2375341 = r2375339 / r2375340;
        return r2375341;
}

↓

double f(double x) {
        double r2375342 = x;
        double r2375343 = 2.0;
        double r2375344 = r2375342 / r2375343;
        double r2375345 = tan(r2375344);
        return r2375345;
}

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

↓

\tan \left(\frac{x}{2}\right)

Original	30.1
Target	0.0
Herbie	0.0

Derivation

Initial program 30.1
\[\frac{1 - \cos x}{\sin x}\]
Simplified0.0
\[\leadsto \color{blue}{\tan \left(\frac{x}{2}\right)}\]
Final simplification0.0
\[\leadsto \tan \left(\frac{x}{2}\right)\]

Reproduce

herbie shell --seed 2019102 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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

Error

Target

Derivation

Reproduce