Average Error: 0.1 → 0.1
Time: 26.3s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\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 r694978 = e;
        double r694979 = v;
        double r694980 = sin(r694979);
        double r694981 = r694978 * r694980;
        double r694982 = 1.0;
        double r694983 = cos(r694979);
        double r694984 = r694978 * r694983;
        double r694985 = r694982 + r694984;
        double r694986 = r694981 / r694985;
        return r694986;
}
↓
double f(double e, double v) {
        double r694987 = e;
        double r694988 = v;
        double r694989 = sin(r694988);
        double r694990 = r694987 * r694989;
        double r694991 = cos(r694988);
        double r694992 = r694991 * r694987;
        double r694993 = 1.0;
        double r694994 = r694992 + r694993;
        double r694995 = r694990 / r694994;
        return r694995;
}

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 2019144 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))