Average Error: 0.1 → 0.1
Time: 8.2s
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 r23896 = e;
        double r23897 = v;
        double r23898 = sin(r23897);
        double r23899 = r23896 * r23898;
        double r23900 = 1.0;
        double r23901 = cos(r23897);
        double r23902 = r23896 * r23901;
        double r23903 = r23900 + r23902;
        double r23904 = r23899 / r23903;
        return r23904;
}
↓
double f(double e, double v) {
        double r23905 = e;
        double r23906 = v;
        double r23907 = sin(r23906);
        double r23908 = r23905 * r23907;
        double r23909 = 1.0;
        double r23910 = cos(r23906);
        double r23911 = r23905 * r23910;
        double r23912 = r23909 + r23911;
        double r23913 = r23908 / r23912;
        return r23913;
}

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 2020062 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))