Average Error: 0.1 → 0.1
Time: 21.8s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1}
double f(double e, double v) {
        double r1277884 = e;
        double r1277885 = v;
        double r1277886 = sin(r1277885);
        double r1277887 = r1277884 * r1277886;
        double r1277888 = 1.0;
        double r1277889 = cos(r1277885);
        double r1277890 = r1277884 * r1277889;
        double r1277891 = r1277888 + r1277890;
        double r1277892 = r1277887 / r1277891;
        return r1277892;
}
↓
double f(double e, double v) {
        double r1277893 = e;
        double r1277894 = v;
        double r1277895 = sin(r1277894);
        double r1277896 = r1277893 * r1277895;
        double r1277897 = cos(r1277894);
        double r1277898 = r1277897 * r1277893;
        double r1277899 = 1.0;
        double r1277900 = r1277898 + r1277899;
        double r1277901 = r1277896 / r1277900;
        return r1277901;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))