Average Error: 0.1 → 0.1
Time: 30.9s
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 r1106920 = e;
        double r1106921 = v;
        double r1106922 = sin(r1106921);
        double r1106923 = r1106920 * r1106922;
        double r1106924 = 1.0;
        double r1106925 = cos(r1106921);
        double r1106926 = r1106920 * r1106925;
        double r1106927 = r1106924 + r1106926;
        double r1106928 = r1106923 / r1106927;
        return r1106928;
}
↓
double f(double e, double v) {
        double r1106929 = e;
        double r1106930 = v;
        double r1106931 = sin(r1106930);
        double r1106932 = r1106929 * r1106931;
        double r1106933 = cos(r1106930);
        double r1106934 = r1106933 * r1106929;
        double r1106935 = 1.0;
        double r1106936 = r1106934 + r1106935;
        double r1106937 = r1106932 / r1106936;
        return r1106937;
}

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 2019138 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))