Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r10181 = e;
        double r10182 = v;
        double r10183 = sin(r10182);
        double r10184 = r10181 * r10183;
        double r10185 = 1.0;
        double r10186 = cos(r10182);
        double r10187 = r10181 * r10186;
        double r10188 = r10185 + r10187;
        double r10189 = r10184 / r10188;
        return r10189;
}
↓
double f(double e, double v) {
        double r10190 = e;
        double r10191 = v;
        double r10192 = sin(r10191);
        double r10193 = r10190 * r10192;
        double r10194 = 1.0;
        double r10195 = cos(r10191);
        double r10196 = r10190 * r10195;
        double r10197 = r10194 + r10196;
        double r10198 = r10193 / r10197;
        return r10198;
}

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

    \[\leadsto \frac{e \cdot \sin v}{1 + e \cdot \cos v}\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))