Average Error: 0.1 → 0.1
Time: 5.8s
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 r15047 = e;
        double r15048 = v;
        double r15049 = sin(r15048);
        double r15050 = r15047 * r15049;
        double r15051 = 1.0;
        double r15052 = cos(r15048);
        double r15053 = r15047 * r15052;
        double r15054 = r15051 + r15053;
        double r15055 = r15050 / r15054;
        return r15055;
}
↓
double f(double e, double v) {
        double r15056 = e;
        double r15057 = v;
        double r15058 = sin(r15057);
        double r15059 = r15056 * r15058;
        double r15060 = 1.0;
        double r15061 = cos(r15057);
        double r15062 = r15056 * r15061;
        double r15063 = r15060 + r15062;
        double r15064 = r15059 / r15063;
        return r15064;
}

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 2020033 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))