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 r14371 = e;
        double r14372 = v;
        double r14373 = sin(r14372);
        double r14374 = r14371 * r14373;
        double r14375 = 1.0;
        double r14376 = cos(r14372);
        double r14377 = r14371 * r14376;
        double r14378 = r14375 + r14377;
        double r14379 = r14374 / r14378;
        return r14379;
}
↓
double f(double e, double v) {
        double r14380 = e;
        double r14381 = v;
        double r14382 = sin(r14381);
        double r14383 = r14380 * r14382;
        double r14384 = 1.0;
        double r14385 = cos(r14381);
        double r14386 = r14380 * r14385;
        double r14387 = r14384 + r14386;
        double r14388 = r14383 / r14387;
        return r14388;
}

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)))))