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 r2450188 = e;
        double r2450189 = v;
        double r2450190 = sin(r2450189);
        double r2450191 = r2450188 * r2450190;
        double r2450192 = 1.0;
        double r2450193 = cos(r2450189);
        double r2450194 = r2450188 * r2450193;
        double r2450195 = r2450192 + r2450194;
        double r2450196 = r2450191 / r2450195;
        return r2450196;
}
↓
double f(double e, double v) {
        double r2450197 = e;
        double r2450198 = v;
        double r2450199 = sin(r2450198);
        double r2450200 = r2450197 * r2450199;
        double r2450201 = cos(r2450198);
        double r2450202 = r2450201 * r2450197;
        double r2450203 = 1.0;
        double r2450204 = r2450202 + r2450203;
        double r2450205 = r2450200 / r2450204;
        return r2450205;
}

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