Average Error: 0.1 → 0.2
Time: 23.2s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\frac{1 + \cos v \cdot e}{\sin v}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{\frac{1 + \cos v \cdot e}{\sin v}}
double f(double e, double v) {
        double r1009393 = e;
        double r1009394 = v;
        double r1009395 = sin(r1009394);
        double r1009396 = r1009393 * r1009395;
        double r1009397 = 1.0;
        double r1009398 = cos(r1009394);
        double r1009399 = r1009393 * r1009398;
        double r1009400 = r1009397 + r1009399;
        double r1009401 = r1009396 / r1009400;
        return r1009401;
}
↓
double f(double e, double v) {
        double r1009402 = e;
        double r1009403 = 1.0;
        double r1009404 = v;
        double r1009405 = cos(r1009404);
        double r1009406 = r1009405 * r1009402;
        double r1009407 = r1009403 + r1009406;
        double r1009408 = sin(r1009404);
        double r1009409 = r1009407 / r1009408;
        double r1009410 = r1009402 / r1009409;
        return r1009410;
}

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*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019141 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))