Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r15027 = e;
        double r15028 = v;
        double r15029 = sin(r15028);
        double r15030 = r15027 * r15029;
        double r15031 = 1.0;
        double r15032 = cos(r15028);
        double r15033 = r15027 * r15032;
        double r15034 = r15031 + r15033;
        double r15035 = r15030 / r15034;
        return r15035;
}
↓
double f(double e, double v) {
        double r15036 = e;
        double r15037 = v;
        double r15038 = sin(r15037);
        double r15039 = r15036 * r15038;
        double r15040 = 1.0;
        double r15041 = cos(r15037);
        double r15042 = r15036 * r15041;
        double r15043 = r15040 + r15042;
        double r15044 = r15039 / r15043;
        return r15044;
}

Error

Bits error versus e

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

  2. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))