Average Error: 0.1 → 0.1
Time: 15.0s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\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 r21157 = e;
        double r21158 = v;
        double r21159 = sin(r21158);
        double r21160 = r21157 * r21159;
        double r21161 = 1.0;
        double r21162 = cos(r21158);
        double r21163 = r21157 * r21162;
        double r21164 = r21161 + r21163;
        double r21165 = r21160 / r21164;
        return r21165;
}
↓
double f(double e, double v) {
        double r21166 = e;
        double r21167 = v;
        double r21168 = sin(r21167);
        double r21169 = r21166 * r21168;
        double r21170 = cos(r21167);
        double r21171 = r21170 * r21166;
        double r21172 = 1.0;
        double r21173 = r21171 + r21172;
        double r21174 = r21169 / r21173;
        return r21174;
}

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 2019196 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))