Average Error: 0.1 → 0.1
Time: 12.7s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + \left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right) \cdot \left(\sqrt[3]{e} \cdot \cos v\right)}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + \left(\sqrt[3]{e} \cdot \sqrt[3]{e}\right) \cdot \left(\sqrt[3]{e} \cdot \cos v\right)}
double f(double e, double v) {
        double r17365 = e;
        double r17366 = v;
        double r17367 = sin(r17366);
        double r17368 = r17365 * r17367;
        double r17369 = 1.0;
        double r17370 = cos(r17366);
        double r17371 = r17365 * r17370;
        double r17372 = r17369 + r17371;
        double r17373 = r17368 / r17372;
        return r17373;
}
↓
double f(double e, double v) {
        double r17374 = e;
        double r17375 = v;
        double r17376 = sin(r17375);
        double r17377 = r17374 * r17376;
        double r17378 = 1.0;
        double r17379 = cbrt(r17374);
        double r17380 = r17379 * r17379;
        double r17381 = cos(r17375);
        double r17382 = r17379 * r17381;
        double r17383 = r17380 * r17382;
        double r17384 = r17378 + r17383;
        double r17385 = r17377 / r17384;
        return r17385;
}

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-cube-cbrt0.1

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

  4. Applied associate-*l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))