Average Error: 0.1 → 0.1
Time: 22.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v}{1 + \cos v \cdot e} \cdot e\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v}{1 + \cos v \cdot e} \cdot e
double f(double e, double v) {
        double r1201221 = e;
        double r1201222 = v;
        double r1201223 = sin(r1201222);
        double r1201224 = r1201221 * r1201223;
        double r1201225 = 1.0;
        double r1201226 = cos(r1201222);
        double r1201227 = r1201221 * r1201226;
        double r1201228 = r1201225 + r1201227;
        double r1201229 = r1201224 / r1201228;
        return r1201229;
}
↓
double f(double e, double v) {
        double r1201230 = v;
        double r1201231 = sin(r1201230);
        double r1201232 = 1.0;
        double r1201233 = cos(r1201230);
        double r1201234 = e;
        double r1201235 = r1201233 * r1201234;
        double r1201236 = r1201232 + r1201235;
        double r1201237 = r1201231 / r1201236;
        double r1201238 = r1201237 * r1201234;
        return r1201238;
}

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 associate-/l*0.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))