Average Error: 0.1 → 0.1
Time: 5.3s
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 r14377 = e;
        double r14378 = v;
        double r14379 = sin(r14378);
        double r14380 = r14377 * r14379;
        double r14381 = 1.0;
        double r14382 = cos(r14378);
        double r14383 = r14377 * r14382;
        double r14384 = r14381 + r14383;
        double r14385 = r14380 / r14384;
        return r14385;
}
↓
double f(double e, double v) {
        double r14386 = e;
        double r14387 = v;
        double r14388 = sin(r14387);
        double r14389 = r14386 * r14388;
        double r14390 = 1.0;
        double r14391 = cos(r14387);
        double r14392 = r14386 * r14391;
        double r14393 = r14390 + r14392;
        double r14394 = r14389 / r14393;
        return r14394;
}

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 2019353 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))