Average Error: 0.1 → 0.1
Time: 8.4s
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 r24753 = e;
        double r24754 = v;
        double r24755 = sin(r24754);
        double r24756 = r24753 * r24755;
        double r24757 = 1.0;
        double r24758 = cos(r24754);
        double r24759 = r24753 * r24758;
        double r24760 = r24757 + r24759;
        double r24761 = r24756 / r24760;
        return r24761;
}
↓
double f(double e, double v) {
        double r24762 = e;
        double r24763 = v;
        double r24764 = sin(r24763);
        double r24765 = r24762 * r24764;
        double r24766 = 1.0;
        double r24767 = cos(r24763);
        double r24768 = r24762 * r24767;
        double r24769 = r24766 + r24768;
        double r24770 = r24765 / r24769;
        return r24770;
}

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 2020089 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))