Average Error: 0.1 → 0.1
Time: 22.9s
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 r1089470 = e;
        double r1089471 = v;
        double r1089472 = sin(r1089471);
        double r1089473 = r1089470 * r1089472;
        double r1089474 = 1.0;
        double r1089475 = cos(r1089471);
        double r1089476 = r1089470 * r1089475;
        double r1089477 = r1089474 + r1089476;
        double r1089478 = r1089473 / r1089477;
        return r1089478;
}
↓
double f(double e, double v) {
        double r1089479 = e;
        double r1089480 = v;
        double r1089481 = sin(r1089480);
        double r1089482 = r1089479 * r1089481;
        double r1089483 = cos(r1089480);
        double r1089484 = r1089483 * r1089479;
        double r1089485 = 1.0;
        double r1089486 = r1089484 + r1089485;
        double r1089487 = r1089482 / r1089486;
        return r1089487;
}

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 2019165 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))