Average Error: 0.1 → 0.1
Time: 19.0s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 \cdot 1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\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)
double f(double e, double v) {
        double r910839 = e;
        double r910840 = v;
        double r910841 = sin(r910840);
        double r910842 = r910839 * r910841;
        double r910843 = 1.0;
        double r910844 = cos(r910840);
        double r910845 = r910839 * r910844;
        double r910846 = r910843 + r910845;
        double r910847 = r910842 / r910846;
        return r910847;
}
↓
double f(double e, double v) {
        double r910848 = e;
        double r910849 = v;
        double r910850 = sin(r910849);
        double r910851 = r910848 * r910850;
        double r910852 = 1.0;
        double r910853 = r910852 * r910852;
        double r910854 = cos(r910849);
        double r910855 = r910848 * r910854;
        double r910856 = r910855 * r910855;
        double r910857 = r910853 - r910856;
        double r910858 = r910851 / r910857;
        double r910859 = r910852 - r910855;
        double r910860 = r910858 * r910859;
        return r910860;
}

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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))