Average Error: 0.1 → 0.1
Time: 33.9s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v}{1 + \cos v \cdot e} \cdot e\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v}{1 + \cos v \cdot e} \cdot e
double f(double e, double v) {
        double r1342708 = e;
        double r1342709 = v;
        double r1342710 = sin(r1342709);
        double r1342711 = r1342708 * r1342710;
        double r1342712 = 1.0;
        double r1342713 = cos(r1342709);
        double r1342714 = r1342708 * r1342713;
        double r1342715 = r1342712 + r1342714;
        double r1342716 = r1342711 / r1342715;
        return r1342716;
}
↓
double f(double e, double v) {
        double r1342717 = v;
        double r1342718 = sin(r1342717);
        double r1342719 = 1.0;
        double r1342720 = cos(r1342717);
        double r1342721 = e;
        double r1342722 = r1342720 * r1342721;
        double r1342723 = r1342719 + r1342722;
        double r1342724 = r1342718 / r1342723;
        double r1342725 = r1342724 * r1342721;
        return r1342725;
}

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 *-un-lft-identity0.1

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019120 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))