Average Error: 0.1 → 0.1
Time: 36.1s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)
double f(double e, double v) {
        double r1226478 = e;
        double r1226479 = v;
        double r1226480 = sin(r1226479);
        double r1226481 = r1226478 * r1226480;
        double r1226482 = 1.0;
        double r1226483 = cos(r1226479);
        double r1226484 = r1226478 * r1226483;
        double r1226485 = r1226482 + r1226484;
        double r1226486 = r1226481 / r1226485;
        return r1226486;
}
↓
double f(double e, double v) {
        double r1226487 = e;
        double r1226488 = v;
        double r1226489 = sin(r1226488);
        double r1226490 = r1226487 * r1226489;
        double r1226491 = 1.0;
        double r1226492 = cos(r1226488);
        double r1226493 = r1226487 * r1226492;
        double r1226494 = r1226493 * r1226493;
        double r1226495 = r1226491 - r1226494;
        double r1226496 = r1226490 / r1226495;
        double r1226497 = r1226491 - r1226493;
        double r1226498 = r1226496 * r1226497;
        return r1226498;
}

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 flip-+0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\frac{1 \cdot 1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)}{1 - e \cdot \cos v}}}\]

  4. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{e \cdot \sin v}{1 \cdot 1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)}\]

  5. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))