Average Error: 0.1 → 0.1
Time: 1.3m
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 r2347282 = e;
        double r2347283 = v;
        double r2347284 = sin(r2347283);
        double r2347285 = r2347282 * r2347284;
        double r2347286 = 1.0;
        double r2347287 = cos(r2347283);
        double r2347288 = r2347282 * r2347287;
        double r2347289 = r2347286 + r2347288;
        double r2347290 = r2347285 / r2347289;
        return r2347290;
}
↓
double f(double e, double v) {
        double r2347291 = e;
        double r2347292 = v;
        double r2347293 = sin(r2347292);
        double r2347294 = r2347291 * r2347293;
        double r2347295 = cos(r2347292);
        double r2347296 = r2347295 * r2347291;
        double r2347297 = 1.0;
        double r2347298 = r2347296 + r2347297;
        double r2347299 = r2347294 / r2347298;
        return r2347299;
}

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 2019124 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))