Average Error: 0.1 → 0.1
Time: 19.0s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\log \left(e^{\cos v \cdot e}\right) + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\log \left(e^{\cos v \cdot e}\right) + 1}
double f(double e, double v) {
        double r444480 = e;
        double r444481 = v;
        double r444482 = sin(r444481);
        double r444483 = r444480 * r444482;
        double r444484 = 1.0;
        double r444485 = cos(r444481);
        double r444486 = r444480 * r444485;
        double r444487 = r444484 + r444486;
        double r444488 = r444483 / r444487;
        return r444488;
}
↓
double f(double e, double v) {
        double r444489 = e;
        double r444490 = v;
        double r444491 = sin(r444490);
        double r444492 = r444489 * r444491;
        double r444493 = cos(r444490);
        double r444494 = r444493 * r444489;
        double r444495 = exp(r444494);
        double r444496 = log(r444495);
        double r444497 = 1.0;
        double r444498 = r444496 + r444497;
        double r444499 = r444492 / r444498;
        return r444499;
}

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. Using strategy rm

  3. Applied add-log-exp0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{\log \left(e^{e \cdot \cos v}\right)}}\]

  4. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{\log \left(e^{\cos v \cdot e}\right) + 1}\]

Reproduce

herbie shell --seed 2019155 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))