Average Error: 0.1 → 0.1
Time: 5.3s
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 r13944 = e;
        double r13945 = v;
        double r13946 = sin(r13945);
        double r13947 = r13944 * r13946;
        double r13948 = 1.0;
        double r13949 = cos(r13945);
        double r13950 = r13944 * r13949;
        double r13951 = r13948 + r13950;
        double r13952 = r13947 / r13951;
        return r13952;
}
↓
double f(double e, double v) {
        double r13953 = e;
        double r13954 = v;
        double r13955 = sin(r13954);
        double r13956 = r13953 * r13955;
        double r13957 = 1.0;
        double r13958 = cos(r13954);
        double r13959 = r13953 * r13958;
        double r13960 = r13957 + r13959;
        double r13961 = r13956 / r13960;
        return r13961;
}

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 2019353 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))