Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{1 + e \cdot \cos v} \cdot \sin v\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{1 + e \cdot \cos v} \cdot \sin v
double f(double e, double v) {
        double r10979 = e;
        double r10980 = v;
        double r10981 = sin(r10980);
        double r10982 = r10979 * r10981;
        double r10983 = 1.0;
        double r10984 = cos(r10980);
        double r10985 = r10979 * r10984;
        double r10986 = r10983 + r10985;
        double r10987 = r10982 / r10986;
        return r10987;
}
↓
double f(double e, double v) {
        double r10988 = e;
        double r10989 = 1.0;
        double r10990 = v;
        double r10991 = cos(r10990);
        double r10992 = r10988 * r10991;
        double r10993 = r10989 + r10992;
        double r10994 = r10988 / r10993;
        double r10995 = sin(r10990);
        double r10996 = r10994 * r10995;
        return r10996;
}

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 associate-/l*0.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))