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 r16128 = e;
        double r16129 = v;
        double r16130 = sin(r16129);
        double r16131 = r16128 * r16130;
        double r16132 = 1.0;
        double r16133 = cos(r16129);
        double r16134 = r16128 * r16133;
        double r16135 = r16132 + r16134;
        double r16136 = r16131 / r16135;
        return r16136;
}
↓
double f(double e, double v) {
        double r16137 = e;
        double r16138 = v;
        double r16139 = sin(r16138);
        double r16140 = r16137 * r16139;
        double r16141 = 1.0;
        double r16142 = cos(r16138);
        double r16143 = r16137 * r16142;
        double r16144 = r16141 + r16143;
        double r16145 = r16140 / r16144;
        return r16145;
}

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 2019346 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))