Average Error: 30.1 → 0
Time: 9.1s
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 r2394070 = 1.0;
        double r2394071 = x;
        double r2394072 = cos(r2394071);
        double r2394073 = r2394070 - r2394072;
        double r2394074 = sin(r2394071);
        double r2394075 = r2394073 / r2394074;
        return r2394075;
}
↓
double f(double x) {
        double r2394076 = x;
        double r2394077 = 2.0;
        double r2394078 = r2394076 / r2394077;
        double r2394079 = tan(r2394078);
        return r2394079;
}

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 2019168 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :herbie-expected 2

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

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