Average Error: 0.1 → 0.1
Time: 6.6s
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 r18795 = e;
        double r18796 = v;
        double r18797 = sin(r18796);
        double r18798 = r18795 * r18797;
        double r18799 = 1.0;
        double r18800 = cos(r18796);
        double r18801 = r18795 * r18800;
        double r18802 = r18799 + r18801;
        double r18803 = r18798 / r18802;
        return r18803;
}
↓
double f(double e, double v) {
        double r18804 = e;
        double r18805 = v;
        double r18806 = sin(r18805);
        double r18807 = r18804 * r18806;
        double r18808 = 1.0;
        double r18809 = cos(r18805);
        double r18810 = r18804 * r18809;
        double r18811 = r18808 + r18810;
        double r18812 = r18807 / r18811;
        return r18812;
}

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 2019346 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))