Average Error: 0.1 → 0.1
Time: 4.8s
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 r11166 = e;
        double r11167 = v;
        double r11168 = sin(r11167);
        double r11169 = r11166 * r11168;
        double r11170 = 1.0;
        double r11171 = cos(r11167);
        double r11172 = r11166 * r11171;
        double r11173 = r11170 + r11172;
        double r11174 = r11169 / r11173;
        return r11174;
}
↓
double f(double e, double v) {
        double r11175 = e;
        double r11176 = v;
        double r11177 = sin(r11176);
        double r11178 = r11175 * r11177;
        double r11179 = 1.0;
        double r11180 = cos(r11176);
        double r11181 = r11175 * r11180;
        double r11182 = r11179 + r11181;
        double r11183 = r11178 / r11182;
        return r11183;
}

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 2020049 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))