Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + \log \left(e^{e \cdot \cos v}\right)}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + \log \left(e^{e \cdot \cos v}\right)}
double f(double e, double v) {
        double r10568 = e;
        double r10569 = v;
        double r10570 = sin(r10569);
        double r10571 = r10568 * r10570;
        double r10572 = 1.0;
        double r10573 = cos(r10569);
        double r10574 = r10568 * r10573;
        double r10575 = r10572 + r10574;
        double r10576 = r10571 / r10575;
        return r10576;
}
↓
double f(double e, double v) {
        double r10577 = e;
        double r10578 = v;
        double r10579 = sin(r10578);
        double r10580 = r10577 * r10579;
        double r10581 = 1.0;
        double r10582 = cos(r10578);
        double r10583 = r10577 * r10582;
        double r10584 = exp(r10583);
        double r10585 = log(r10584);
        double r10586 = r10581 + r10585;
        double r10587 = r10580 / r10586;
        return r10587;
}

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

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

Reproduce

herbie shell --seed 2020036 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))