Average Error: 0.1 → 0.1
Time: 21.4s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + \sqrt[3]{{\left(e \cdot \cos v\right)}^{3}}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + \sqrt[3]{{\left(e \cdot \cos v\right)}^{3}}}
double f(double e, double v) {
        double r21448 = e;
        double r21449 = v;
        double r21450 = sin(r21449);
        double r21451 = r21448 * r21450;
        double r21452 = 1.0;
        double r21453 = cos(r21449);
        double r21454 = r21448 * r21453;
        double r21455 = r21452 + r21454;
        double r21456 = r21451 / r21455;
        return r21456;
}
↓
double f(double e, double v) {
        double r21457 = e;
        double r21458 = v;
        double r21459 = sin(r21458);
        double r21460 = r21457 * r21459;
        double r21461 = 1.0;
        double r21462 = cos(r21458);
        double r21463 = r21457 * r21462;
        double r21464 = 3.0;
        double r21465 = pow(r21463, r21464);
        double r21466 = cbrt(r21465);
        double r21467 = r21461 + r21466;
        double r21468 = r21460 / r21467;
        return r21468;
}

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-cbrt-cube0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + e \cdot \color{blue}{\sqrt[3]{\left(\cos v \cdot \cos v\right) \cdot \cos v}}}\]

  4. Applied add-cbrt-cube0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{\sqrt[3]{\left(e \cdot e\right) \cdot e}} \cdot \sqrt[3]{\left(\cos v \cdot \cos v\right) \cdot \cos v}}\]

  5. Applied cbrt-unprod0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{\sqrt[3]{\left(\left(e \cdot e\right) \cdot e\right) \cdot \left(\left(\cos v \cdot \cos v\right) \cdot \cos v\right)}}}\]

  6. Simplified0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \sqrt[3]{\color{blue}{{\left(e \cdot \cos v\right)}^{3}}}}\]

  7. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \sqrt[3]{{\left(e \cdot \cos v\right)}^{3}}}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))