Average Error: 0.1 → 0.1
Time: 44.7s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1}
double f(double e, double v) {
        double r1849039 = e;
        double r1849040 = v;
        double r1849041 = sin(r1849040);
        double r1849042 = r1849039 * r1849041;
        double r1849043 = 1.0;
        double r1849044 = cos(r1849040);
        double r1849045 = r1849039 * r1849044;
        double r1849046 = r1849043 + r1849045;
        double r1849047 = r1849042 / r1849046;
        return r1849047;
}
↓
double f(double e, double v) {
        double r1849048 = e;
        double r1849049 = v;
        double r1849050 = sin(r1849049);
        double r1849051 = r1849048 * r1849050;
        double r1849052 = cos(r1849049);
        double r1849053 = r1849052 * r1849048;
        double r1849054 = 1.0;
        double r1849055 = r1849053 + r1849054;
        double r1849056 = r1849051 / r1849055;
        return r1849056;
}

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

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

Reproduce

herbie shell --seed 2019125 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))