Average Error: 30.2 → 0
Time: 11.3s
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 r507224 = 1.0;
        double r507225 = x;
        double r507226 = cos(r507225);
        double r507227 = r507224 - r507226;
        double r507228 = sin(r507225);
        double r507229 = r507227 / r507228;
        return r507229;
}
↓
double f(double x) {
        double r507230 = x;
        double r507231 = 2.0;
        double r507232 = r507230 / r507231;
        double r507233 = tan(r507232);
        return r507233;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 30.2

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

  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 2019156 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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