Average Error: 0.1 → 0.1
Time: 21.3s
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 r1385040 = e;
        double r1385041 = v;
        double r1385042 = sin(r1385041);
        double r1385043 = r1385040 * r1385042;
        double r1385044 = 1.0;
        double r1385045 = cos(r1385041);
        double r1385046 = r1385040 * r1385045;
        double r1385047 = r1385044 + r1385046;
        double r1385048 = r1385043 / r1385047;
        return r1385048;
}
↓
double f(double e, double v) {
        double r1385049 = e;
        double r1385050 = v;
        double r1385051 = sin(r1385050);
        double r1385052 = r1385049 * r1385051;
        double r1385053 = cos(r1385050);
        double r1385054 = r1385053 * r1385049;
        double r1385055 = 1.0;
        double r1385056 = r1385054 + r1385055;
        double r1385057 = r1385052 / r1385056;
        return r1385057;
}

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 2019163 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))