Average Error: 0.1 → 0.1
Time: 1.4m
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 r2773785 = e;
        double r2773786 = v;
        double r2773787 = sin(r2773786);
        double r2773788 = r2773785 * r2773787;
        double r2773789 = 1.0;
        double r2773790 = cos(r2773786);
        double r2773791 = r2773785 * r2773790;
        double r2773792 = r2773789 + r2773791;
        double r2773793 = r2773788 / r2773792;
        return r2773793;
}
↓
double f(double e, double v) {
        double r2773794 = e;
        double r2773795 = v;
        double r2773796 = sin(r2773795);
        double r2773797 = r2773794 * r2773796;
        double r2773798 = cos(r2773795);
        double r2773799 = r2773798 * r2773794;
        double r2773800 = 1.0;
        double r2773801 = r2773799 + r2773800;
        double r2773802 = r2773797 / r2773801;
        return r2773802;
}

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 2019121 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))