Average Error: 0.1 → 0.1
Time: 29.1s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\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 r1079388 = e;
        double r1079389 = v;
        double r1079390 = sin(r1079389);
        double r1079391 = r1079388 * r1079390;
        double r1079392 = 1.0;
        double r1079393 = cos(r1079389);
        double r1079394 = r1079388 * r1079393;
        double r1079395 = r1079392 + r1079394;
        double r1079396 = r1079391 / r1079395;
        return r1079396;
}
↓
double f(double e, double v) {
        double r1079397 = e;
        double r1079398 = v;
        double r1079399 = sin(r1079398);
        double r1079400 = r1079397 * r1079399;
        double r1079401 = cos(r1079398);
        double r1079402 = r1079401 * r1079397;
        double r1079403 = 1.0;
        double r1079404 = r1079402 + r1079403;
        double r1079405 = r1079400 / r1079404;
        return r1079405;
}

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 2019169 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))