Average Error: 0.1 → 0.1
Time: 49.3s
Precision: 64
\[0.0 \le e \le 1.0\]
\[\frac{e \cdot \sin v}{1.0 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1.0}\]
\frac{e \cdot \sin v}{1.0 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1.0}
double f(double e, double v) {
        double r1098117 = e;
        double r1098118 = v;
        double r1098119 = sin(r1098118);
        double r1098120 = r1098117 * r1098119;
        double r1098121 = 1.0;
        double r1098122 = cos(r1098118);
        double r1098123 = r1098117 * r1098122;
        double r1098124 = r1098121 + r1098123;
        double r1098125 = r1098120 / r1098124;
        return r1098125;
}
↓
double f(double e, double v) {
        double r1098126 = e;
        double r1098127 = v;
        double r1098128 = sin(r1098127);
        double r1098129 = r1098126 * r1098128;
        double r1098130 = cos(r1098127);
        double r1098131 = r1098130 * r1098126;
        double r1098132 = 1.0;
        double r1098133 = r1098131 + r1098132;
        double r1098134 = r1098129 / r1098133;
        return r1098134;
}

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

    \[\frac{e \cdot \sin v}{1.0 + e \cdot \cos v}\]

  2. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{\cos v \cdot e + 1.0}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))