Average Error: 0.1 → 0.1
Time: 34.7s
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 r1359904 = e;
        double r1359905 = v;
        double r1359906 = sin(r1359905);
        double r1359907 = r1359904 * r1359906;
        double r1359908 = 1.0;
        double r1359909 = cos(r1359905);
        double r1359910 = r1359904 * r1359909;
        double r1359911 = r1359908 + r1359910;
        double r1359912 = r1359907 / r1359911;
        return r1359912;
}
↓
double f(double e, double v) {
        double r1359913 = e;
        double r1359914 = v;
        double r1359915 = sin(r1359914);
        double r1359916 = r1359913 * r1359915;
        double r1359917 = 1.0;
        double r1359918 = cos(r1359914);
        double r1359919 = r1359913 * r1359918;
        double r1359920 = r1359919 * r1359919;
        double r1359921 = r1359917 - r1359920;
        double r1359922 = r1359916 / r1359921;
        double r1359923 = r1359917 - r1359919;
        double r1359924 = r1359922 * r1359923;
        return r1359924;
}

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