Average Error: 0.1 → 0.1
Time: 16.0s
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 r23070 = e;
        double r23071 = v;
        double r23072 = sin(r23071);
        double r23073 = r23070 * r23072;
        double r23074 = 1.0;
        double r23075 = cos(r23071);
        double r23076 = r23070 * r23075;
        double r23077 = r23074 + r23076;
        double r23078 = r23073 / r23077;
        return r23078;
}
↓
double f(double e, double v) {
        double r23079 = e;
        double r23080 = v;
        double r23081 = sin(r23080);
        double r23082 = r23079 * r23081;
        double r23083 = 1.0;
        double r23084 = cos(r23080);
        double r23085 = r23079 * r23084;
        double r23086 = r23083 + r23085;
        double r23087 = r23082 / r23086;
        return r23087;
}

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 2019209 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))