Average Error: 0.1 → 0.1
Time: 4.6s
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 r12102 = e;
        double r12103 = v;
        double r12104 = sin(r12103);
        double r12105 = r12102 * r12104;
        double r12106 = 1.0;
        double r12107 = cos(r12103);
        double r12108 = r12102 * r12107;
        double r12109 = r12106 + r12108;
        double r12110 = r12105 / r12109;
        return r12110;
}
↓
double f(double e, double v) {
        double r12111 = e;
        double r12112 = v;
        double r12113 = sin(r12112);
        double r12114 = r12111 * r12113;
        double r12115 = 1.0;
        double r12116 = cos(r12112);
        double r12117 = r12111 * r12116;
        double r12118 = r12115 + r12117;
        double r12119 = r12114 / r12118;
        return r12119;
}

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 2020062 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))