Average Error: 0.1 → 0.1
Time: 16.0s
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 r519322 = e;
        double r519323 = v;
        double r519324 = sin(r519323);
        double r519325 = r519322 * r519324;
        double r519326 = 1.0;
        double r519327 = cos(r519323);
        double r519328 = r519322 * r519327;
        double r519329 = r519326 + r519328;
        double r519330 = r519325 / r519329;
        return r519330;
}
↓
double f(double e, double v) {
        double r519331 = e;
        double r519332 = v;
        double r519333 = sin(r519332);
        double r519334 = r519331 * r519333;
        double r519335 = cos(r519332);
        double r519336 = r519335 * r519331;
        double r519337 = 1.0;
        double r519338 = r519336 + r519337;
        double r519339 = r519334 / r519338;
        return r519339;
}

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 2019156 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))