Average Error: 0.1 → 0.1
Time: 16.7s
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 r413729 = e;
        double r413730 = v;
        double r413731 = sin(r413730);
        double r413732 = r413729 * r413731;
        double r413733 = 1.0;
        double r413734 = cos(r413730);
        double r413735 = r413729 * r413734;
        double r413736 = r413733 + r413735;
        double r413737 = r413732 / r413736;
        return r413737;
}
↓
double f(double e, double v) {
        double r413738 = e;
        double r413739 = v;
        double r413740 = sin(r413739);
        double r413741 = r413738 * r413740;
        double r413742 = cos(r413739);
        double r413743 = r413742 * r413738;
        double r413744 = 1.0;
        double r413745 = r413743 + r413744;
        double r413746 = r413741 / r413745;
        return r413746;
}

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 2019128 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))