Average Error: 0.1 → 0.1
Time: 32.6s
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 r1025268 = e;
        double r1025269 = v;
        double r1025270 = sin(r1025269);
        double r1025271 = r1025268 * r1025270;
        double r1025272 = 1.0;
        double r1025273 = cos(r1025269);
        double r1025274 = r1025268 * r1025273;
        double r1025275 = r1025272 + r1025274;
        double r1025276 = r1025271 / r1025275;
        return r1025276;
}
↓
double f(double e, double v) {
        double r1025277 = e;
        double r1025278 = v;
        double r1025279 = sin(r1025278);
        double r1025280 = r1025277 * r1025279;
        double r1025281 = cos(r1025278);
        double r1025282 = r1025281 * r1025277;
        double r1025283 = 1.0;
        double r1025284 = r1025282 + r1025283;
        double r1025285 = r1025280 / r1025284;
        return r1025285;
}

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 2019143 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))