Average Error: 0.1 → 0.1
Time: 39.0s
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 r1451230 = e;
        double r1451231 = v;
        double r1451232 = sin(r1451231);
        double r1451233 = r1451230 * r1451232;
        double r1451234 = 1.0;
        double r1451235 = cos(r1451231);
        double r1451236 = r1451230 * r1451235;
        double r1451237 = r1451234 + r1451236;
        double r1451238 = r1451233 / r1451237;
        return r1451238;
}
↓
double f(double e, double v) {
        double r1451239 = e;
        double r1451240 = v;
        double r1451241 = sin(r1451240);
        double r1451242 = r1451239 * r1451241;
        double r1451243 = cos(r1451240);
        double r1451244 = r1451243 * r1451239;
        double r1451245 = 1.0;
        double r1451246 = r1451244 + r1451245;
        double r1451247 = r1451242 / r1451246;
        return r1451247;
}

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 2019128 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))