Average Error: 0.1 → 0.1
Time: 21.1s
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 r1114387 = e;
        double r1114388 = v;
        double r1114389 = sin(r1114388);
        double r1114390 = r1114387 * r1114389;
        double r1114391 = 1.0;
        double r1114392 = cos(r1114388);
        double r1114393 = r1114387 * r1114392;
        double r1114394 = r1114391 + r1114393;
        double r1114395 = r1114390 / r1114394;
        return r1114395;
}
↓
double f(double e, double v) {
        double r1114396 = e;
        double r1114397 = v;
        double r1114398 = sin(r1114397);
        double r1114399 = r1114396 * r1114398;
        double r1114400 = cos(r1114397);
        double r1114401 = r1114400 * r1114396;
        double r1114402 = 1.0;
        double r1114403 = r1114401 + r1114402;
        double r1114404 = r1114399 / r1114403;
        return r1114404;
}

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 2019163 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))