Average Error: 0.1 → 0.1
Time: 19.9s
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 r945901 = e;
        double r945902 = v;
        double r945903 = sin(r945902);
        double r945904 = r945901 * r945903;
        double r945905 = 1.0;
        double r945906 = cos(r945902);
        double r945907 = r945901 * r945906;
        double r945908 = r945905 + r945907;
        double r945909 = r945904 / r945908;
        return r945909;
}
↓
double f(double e, double v) {
        double r945910 = e;
        double r945911 = v;
        double r945912 = sin(r945911);
        double r945913 = r945910 * r945912;
        double r945914 = cos(r945911);
        double r945915 = r945914 * r945910;
        double r945916 = 1.0;
        double r945917 = r945915 + r945916;
        double r945918 = r945913 / r945917;
        return r945918;
}

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)))))