Average Error: 0.1 → 0.1
Time: 19.9s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\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 r1188341 = e;
        double r1188342 = v;
        double r1188343 = sin(r1188342);
        double r1188344 = r1188341 * r1188343;
        double r1188345 = 1.0;
        double r1188346 = cos(r1188342);
        double r1188347 = r1188341 * r1188346;
        double r1188348 = r1188345 + r1188347;
        double r1188349 = r1188344 / r1188348;
        return r1188349;
}
↓
double f(double e, double v) {
        double r1188350 = e;
        double r1188351 = v;
        double r1188352 = sin(r1188351);
        double r1188353 = r1188350 * r1188352;
        double r1188354 = cos(r1188351);
        double r1188355 = r1188354 * r1188350;
        double r1188356 = 1.0;
        double r1188357 = r1188355 + r1188356;
        double r1188358 = r1188353 / r1188357;
        return r1188358;
}

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 2019163 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))