Average Error: 0.1 → 0.1
Time: 30.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1}
double f(double e, double v) {
        double r1643987 = e;
        double r1643988 = v;
        double r1643989 = sin(r1643988);
        double r1643990 = r1643987 * r1643989;
        double r1643991 = 1.0;
        double r1643992 = cos(r1643988);
        double r1643993 = r1643987 * r1643992;
        double r1643994 = r1643991 + r1643993;
        double r1643995 = r1643990 / r1643994;
        return r1643995;
}
↓
double f(double e, double v) {
        double r1643996 = e;
        double r1643997 = v;
        double r1643998 = sin(r1643997);
        double r1643999 = r1643996 * r1643998;
        double r1644000 = cos(r1643997);
        double r1644001 = r1644000 * r1643996;
        double r1644002 = 1.0;
        double r1644003 = r1644001 + r1644002;
        double r1644004 = r1643999 / r1644003;
        return r1644004;
}

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

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

Reproduce

herbie shell --seed 2019179 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))