Average Error: 0.1 → 0.1
Time: 32.6s
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 r1033976 = e;
        double r1033977 = v;
        double r1033978 = sin(r1033977);
        double r1033979 = r1033976 * r1033978;
        double r1033980 = 1.0;
        double r1033981 = cos(r1033977);
        double r1033982 = r1033976 * r1033981;
        double r1033983 = r1033980 + r1033982;
        double r1033984 = r1033979 / r1033983;
        return r1033984;
}
↓
double f(double e, double v) {
        double r1033985 = e;
        double r1033986 = v;
        double r1033987 = sin(r1033986);
        double r1033988 = r1033985 * r1033987;
        double r1033989 = 1.0;
        double r1033990 = cos(r1033986);
        double r1033991 = r1033985 * r1033990;
        double r1033992 = r1033991 * r1033991;
        double r1033993 = r1033989 - r1033992;
        double r1033994 = r1033988 / r1033993;
        double r1033995 = r1033989 - r1033991;
        double r1033996 = r1033994 * r1033995;
        return r1033996;
}

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 2019104 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))