Average Error: 0.1 → 0.1
Time: 5.3s
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 r12168 = e;
        double r12169 = v;
        double r12170 = sin(r12169);
        double r12171 = r12168 * r12170;
        double r12172 = 1.0;
        double r12173 = cos(r12169);
        double r12174 = r12168 * r12173;
        double r12175 = r12172 + r12174;
        double r12176 = r12171 / r12175;
        return r12176;
}
↓
double f(double e, double v) {
        double r12177 = e;
        double r12178 = v;
        double r12179 = sin(r12178);
        double r12180 = r12177 * r12179;
        double r12181 = 1.0;
        double r12182 = cos(r12178);
        double r12183 = r12177 * r12182;
        double r12184 = r12181 + r12183;
        double r12185 = r12180 / r12184;
        return r12185;
}

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 2020001 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))