Average Error: 0.1 → 0.1
Time: 21.5s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(\frac{e}{1 - \left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)} \cdot \sin v\right) \cdot \left(1 - \cos v \cdot e\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\left(\frac{e}{1 - \left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)} \cdot \sin v\right) \cdot \left(1 - \cos v \cdot e\right)
double f(double e, double v) {
        double r470841 = e;
        double r470842 = v;
        double r470843 = sin(r470842);
        double r470844 = r470841 * r470843;
        double r470845 = 1.0;
        double r470846 = cos(r470842);
        double r470847 = r470841 * r470846;
        double r470848 = r470845 + r470847;
        double r470849 = r470844 / r470848;
        return r470849;
}
↓
double f(double e, double v) {
        double r470850 = e;
        double r470851 = 1.0;
        double r470852 = v;
        double r470853 = cos(r470852);
        double r470854 = r470853 * r470850;
        double r470855 = r470854 * r470854;
        double r470856 = r470851 - r470855;
        double r470857 = r470850 / r470856;
        double r470858 = sin(r470852);
        double r470859 = r470857 * r470858;
        double r470860 = r470851 - r470854;
        double r470861 = r470859 * r470860;
        return r470861;
}

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. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))