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 r11635 = e;
        double r11636 = v;
        double r11637 = sin(r11636);
        double r11638 = r11635 * r11637;
        double r11639 = 1.0;
        double r11640 = cos(r11636);
        double r11641 = r11635 * r11640;
        double r11642 = r11639 + r11641;
        double r11643 = r11638 / r11642;
        return r11643;
}
↓
double f(double e, double v) {
        double r11644 = e;
        double r11645 = 1.0;
        double r11646 = v;
        double r11647 = cos(r11646);
        double r11648 = r11644 * r11647;
        double r11649 = r11645 + r11648;
        double r11650 = r11644 / r11649;
        double r11651 = sin(r11646);
        double r11652 = r11650 * r11651;
        return r11652;
}

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 2020003 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))