Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r11952 = e;
        double r11953 = v;
        double r11954 = sin(r11953);
        double r11955 = r11952 * r11954;
        double r11956 = 1.0;
        double r11957 = cos(r11953);
        double r11958 = r11952 * r11957;
        double r11959 = r11956 + r11958;
        double r11960 = r11955 / r11959;
        return r11960;
}
↓
double f(double e, double v) {
        double r11961 = e;
        double r11962 = v;
        double r11963 = sin(r11962);
        double r11964 = r11961 * r11963;
        double r11965 = 1.0;
        double r11966 = cos(r11962);
        double r11967 = r11961 * r11966;
        double r11968 = r11965 + r11967;
        double r11969 = r11964 / r11968;
        return r11969;
}

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

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))