Average Error: 0.1 → 0.2
Time: 18.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\sqrt[3]{1 + \cos v \cdot e} \cdot \sqrt[3]{1 + \cos v \cdot e}} \cdot \frac{\sin v}{\sqrt[3]{1 + \cos v \cdot e}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{\sqrt[3]{1 + \cos v \cdot e} \cdot \sqrt[3]{1 + \cos v \cdot e}} \cdot \frac{\sin v}{\sqrt[3]{1 + \cos v \cdot e}}
double f(double e, double v) {
        double r25397 = e;
        double r25398 = v;
        double r25399 = sin(r25398);
        double r25400 = r25397 * r25399;
        double r25401 = 1.0;
        double r25402 = cos(r25398);
        double r25403 = r25397 * r25402;
        double r25404 = r25401 + r25403;
        double r25405 = r25400 / r25404;
        return r25405;
}
↓
double f(double e, double v) {
        double r25406 = e;
        double r25407 = 1.0;
        double r25408 = v;
        double r25409 = cos(r25408);
        double r25410 = r25409 * r25406;
        double r25411 = r25407 + r25410;
        double r25412 = cbrt(r25411);
        double r25413 = r25412 * r25412;
        double r25414 = r25406 / r25413;
        double r25415 = sin(r25408);
        double r25416 = r25415 / r25412;
        double r25417 = r25414 * r25416;
        return r25417;
}

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-cbrt0.2

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))