Average Error: 0.1 → 0.1
Time: 5.4s
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 r13365 = e;
        double r13366 = v;
        double r13367 = sin(r13366);
        double r13368 = r13365 * r13367;
        double r13369 = 1.0;
        double r13370 = cos(r13366);
        double r13371 = r13365 * r13370;
        double r13372 = r13369 + r13371;
        double r13373 = r13368 / r13372;
        return r13373;
}
↓
double f(double e, double v) {
        double r13374 = e;
        double r13375 = v;
        double r13376 = sin(r13375);
        double r13377 = r13374 * r13376;
        double r13378 = 1.0;
        double r13379 = cos(r13375);
        double r13380 = r13374 * r13379;
        double r13381 = r13378 + r13380;
        double r13382 = r13377 / r13381;
        return r13382;
}

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 2019362 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))