Average Error: 0.1 → 0.2
Time: 19.6s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\frac{e \cdot \sin v}{\sqrt{\cos v \cdot e + 1}}}{\sqrt{\cos v \cdot e + 1}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\frac{e \cdot \sin v}{\sqrt{\cos v \cdot e + 1}}}{\sqrt{\cos v \cdot e + 1}}
double f(double e, double v) {
        double r653340 = e;
        double r653341 = v;
        double r653342 = sin(r653341);
        double r653343 = r653340 * r653342;
        double r653344 = 1.0;
        double r653345 = cos(r653341);
        double r653346 = r653340 * r653345;
        double r653347 = r653344 + r653346;
        double r653348 = r653343 / r653347;
        return r653348;
}
↓
double f(double e, double v) {
        double r653349 = e;
        double r653350 = v;
        double r653351 = sin(r653350);
        double r653352 = r653349 * r653351;
        double r653353 = cos(r653350);
        double r653354 = r653353 * r653349;
        double r653355 = 1.0;
        double r653356 = r653354 + r653355;
        double r653357 = sqrt(r653356);
        double r653358 = r653352 / r653357;
        double r653359 = r653358 / r653357;
        return r653359;
}

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-sqr-sqrt0.2

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

  4. Applied associate-/r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019130 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))