Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{1 + e \cdot \cos v} \cdot \sin v\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{1 + e \cdot \cos v} \cdot \sin v
double f(double e, double v) {
        double r11094 = e;
        double r11095 = v;
        double r11096 = sin(r11095);
        double r11097 = r11094 * r11096;
        double r11098 = 1.0;
        double r11099 = cos(r11095);
        double r11100 = r11094 * r11099;
        double r11101 = r11098 + r11100;
        double r11102 = r11097 / r11101;
        return r11102;
}
↓
double f(double e, double v) {
        double r11103 = e;
        double r11104 = 1.0;
        double r11105 = v;
        double r11106 = cos(r11105);
        double r11107 = r11103 * r11106;
        double r11108 = r11104 + r11107;
        double r11109 = r11103 / r11108;
        double r11110 = sin(r11105);
        double r11111 = r11109 * r11110;
        return r11111;
}

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. Using strategy rm

  3. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))