Average Error: 0.1 → 0.1
Time: 23.3s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r31737 = e;
        double r31738 = v;
        double r31739 = sin(r31738);
        double r31740 = r31737 * r31739;
        double r31741 = 1.0;
        double r31742 = cos(r31738);
        double r31743 = r31737 * r31742;
        double r31744 = r31741 + r31743;
        double r31745 = r31740 / r31744;
        return r31745;
}
↓
double f(double e, double v) {
        double r31746 = e;
        double r31747 = v;
        double r31748 = sin(r31747);
        double r31749 = r31746 * r31748;
        double r31750 = 1.0;
        double r31751 = cos(r31747);
        double r31752 = r31746 * r31751;
        double r31753 = r31750 + r31752;
        double r31754 = r31749 / r31753;
        return r31754;
}

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

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

Reproduce

herbie shell --seed 2019304 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))