Average Error: 0.1 → 0.1
Time: 21.1s
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 r21526 = e;
        double r21527 = v;
        double r21528 = sin(r21527);
        double r21529 = r21526 * r21528;
        double r21530 = 1.0;
        double r21531 = cos(r21527);
        double r21532 = r21526 * r21531;
        double r21533 = r21530 + r21532;
        double r21534 = r21529 / r21533;
        return r21534;
}
↓
double f(double e, double v) {
        double r21535 = e;
        double r21536 = v;
        double r21537 = sin(r21536);
        double r21538 = r21535 * r21537;
        double r21539 = 1.0;
        double r21540 = cos(r21536);
        double r21541 = r21535 * r21540;
        double r21542 = 3.0;
        double r21543 = pow(r21541, r21542);
        double r21544 = cbrt(r21543);
        double r21545 = r21539 + r21544;
        double r21546 = r21538 / r21545;
        return r21546;
}

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)))))