Average Error: 0.1 → 0.1
Time: 19.5s
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 r978572 = e;
        double r978573 = v;
        double r978574 = sin(r978573);
        double r978575 = r978572 * r978574;
        double r978576 = 1.0;
        double r978577 = cos(r978573);
        double r978578 = r978572 * r978577;
        double r978579 = r978576 + r978578;
        double r978580 = r978575 / r978579;
        return r978580;
}
↓
double f(double e, double v) {
        double r978581 = e;
        double r978582 = v;
        double r978583 = sin(r978582);
        double r978584 = r978581 * r978583;
        double r978585 = cos(r978582);
        double r978586 = r978585 * r978581;
        double r978587 = 1.0;
        double r978588 = r978586 + r978587;
        double r978589 = r978584 / r978588;
        return r978589;
}

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 2019164 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))