Average Error: 0.1 → 0.1
Time: 6.3s
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 r18135 = e;
        double r18136 = v;
        double r18137 = sin(r18136);
        double r18138 = r18135 * r18137;
        double r18139 = 1.0;
        double r18140 = cos(r18136);
        double r18141 = r18135 * r18140;
        double r18142 = r18139 + r18141;
        double r18143 = r18138 / r18142;
        return r18143;
}
↓
double f(double e, double v) {
        double r18144 = e;
        double r18145 = v;
        double r18146 = sin(r18145);
        double r18147 = r18144 * r18146;
        double r18148 = 1.0;
        double r18149 = cos(r18145);
        double r18150 = r18144 * r18149;
        double r18151 = r18148 + r18150;
        double r18152 = r18147 / r18151;
        return r18152;
}

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 2020001 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))