Average Error: 0.1 → 0.1
Time: 43.5s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\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 r1754646 = e;
        double r1754647 = v;
        double r1754648 = sin(r1754647);
        double r1754649 = r1754646 * r1754648;
        double r1754650 = 1.0;
        double r1754651 = cos(r1754647);
        double r1754652 = r1754646 * r1754651;
        double r1754653 = r1754650 + r1754652;
        double r1754654 = r1754649 / r1754653;
        return r1754654;
}
↓
double f(double e, double v) {
        double r1754655 = e;
        double r1754656 = v;
        double r1754657 = sin(r1754656);
        double r1754658 = r1754655 * r1754657;
        double r1754659 = cos(r1754656);
        double r1754660 = r1754659 * r1754655;
        double r1754661 = 1.0;
        double r1754662 = r1754660 + r1754661;
        double r1754663 = r1754658 / r1754662;
        return r1754663;
}

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 2019128 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))