Average Error: 0.1 → 0.1
Time: 18.7s
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 r813438 = e;
        double r813439 = v;
        double r813440 = sin(r813439);
        double r813441 = r813438 * r813440;
        double r813442 = 1.0;
        double r813443 = cos(r813439);
        double r813444 = r813438 * r813443;
        double r813445 = r813442 + r813444;
        double r813446 = r813441 / r813445;
        return r813446;
}
↓
double f(double e, double v) {
        double r813447 = e;
        double r813448 = v;
        double r813449 = sin(r813448);
        double r813450 = r813447 * r813449;
        double r813451 = 1.0;
        double r813452 = cos(r813448);
        double r813453 = r813447 * r813452;
        double r813454 = r813453 * r813453;
        double r813455 = r813451 - r813454;
        double r813456 = r813450 / r813455;
        double r813457 = r813451 - r813453;
        double r813458 = r813456 * r813457;
        return r813458;
}

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 2019168 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))