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 r11119 = e;
        double r11120 = v;
        double r11121 = sin(r11120);
        double r11122 = r11119 * r11121;
        double r11123 = 1.0;
        double r11124 = cos(r11120);
        double r11125 = r11119 * r11124;
        double r11126 = r11123 + r11125;
        double r11127 = r11122 / r11126;
        return r11127;
}
↓
double f(double e, double v) {
        double r11128 = e;
        double r11129 = v;
        double r11130 = sin(r11129);
        double r11131 = r11128 * r11130;
        double r11132 = 1.0;
        double r11133 = cos(r11129);
        double r11134 = r11128 * r11133;
        double r11135 = r11132 + r11134;
        double r11136 = r11131 / r11135;
        return r11136;
}

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 2020060 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))