Average Error: 0.1 → 0.1
Time: 18.9s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1}
double f(double e, double v) {
        double r34587 = e;
        double r34588 = v;
        double r34589 = sin(r34588);
        double r34590 = r34587 * r34589;
        double r34591 = 1.0;
        double r34592 = cos(r34588);
        double r34593 = r34587 * r34592;
        double r34594 = r34591 + r34593;
        double r34595 = r34590 / r34594;
        return r34595;
}
↓
double f(double e, double v) {
        double r34596 = e;
        double r34597 = v;
        double r34598 = sin(r34597);
        double r34599 = r34596 * r34598;
        double r34600 = cos(r34597);
        double r34601 = r34600 * r34596;
        double r34602 = 1.0;
        double r34603 = r34601 + r34602;
        double r34604 = r34599 / r34603;
        return r34604;
}

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

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

Reproduce

herbie shell --seed 2019179 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))