Average Error: 0.1 → 0.1
Time: 5.4s
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 r13950 = e;
        double r13951 = v;
        double r13952 = sin(r13951);
        double r13953 = r13950 * r13952;
        double r13954 = 1.0;
        double r13955 = cos(r13951);
        double r13956 = r13950 * r13955;
        double r13957 = r13954 + r13956;
        double r13958 = r13953 / r13957;
        return r13958;
}
↓
double f(double e, double v) {
        double r13959 = e;
        double r13960 = v;
        double r13961 = sin(r13960);
        double r13962 = r13959 * r13961;
        double r13963 = 1.0;
        double r13964 = cos(r13960);
        double r13965 = r13959 * r13964;
        double r13966 = r13963 + r13965;
        double r13967 = r13962 / r13966;
        return r13967;
}

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)))))