Average Error: 30.2 → 0.0
Time: 11.8s
Precision: 64
\[\frac{1 - \cos x}{\sin x}\]
↓
\[\tan \left(\frac{x}{2}\right)\]
double f(double x) {
        double r1892014 = 1.0;
        double r1892015 = x;
        double r1892016 = cos(r1892015);
        double r1892017 = r1892014 - r1892016;
        double r1892018 = sin(r1892015);
        double r1892019 = r1892017 / r1892018;
        return r1892019;
}
↓
double f(double x) {
        double r1892020 = x;
        double r1892021 = 2.0;
        double r1892022 = r1892020 / r1892021;
        double r1892023 = tan(r1892022);
        return r1892023;
}


\frac{1 - \cos x}{\sin x}
↓
\tan \left(\frac{x}{2}\right)

Error

Bits error versus x

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 2019101 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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