Average Error: 0.1 → 0.1
Time: 44.8s
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 r1329297 = e;
        double r1329298 = v;
        double r1329299 = sin(r1329298);
        double r1329300 = r1329297 * r1329299;
        double r1329301 = 1.0;
        double r1329302 = cos(r1329298);
        double r1329303 = r1329297 * r1329302;
        double r1329304 = r1329301 + r1329303;
        double r1329305 = r1329300 / r1329304;
        return r1329305;
}
↓
double f(double e, double v) {
        double r1329306 = e;
        double r1329307 = v;
        double r1329308 = sin(r1329307);
        double r1329309 = r1329306 * r1329308;
        double r1329310 = cos(r1329307);
        double r1329311 = r1329310 * r1329306;
        double r1329312 = 1.0;
        double r1329313 = r1329311 + r1329312;
        double r1329314 = r1329309 / r1329313;
        return r1329314;
}

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 2019149 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))