Average Error: 0.1 → 0.1
Time: 23.2s
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 r1201219 = e;
        double r1201220 = v;
        double r1201221 = sin(r1201220);
        double r1201222 = r1201219 * r1201221;
        double r1201223 = 1.0;
        double r1201224 = cos(r1201220);
        double r1201225 = r1201219 * r1201224;
        double r1201226 = r1201223 + r1201225;
        double r1201227 = r1201222 / r1201226;
        return r1201227;
}
↓
double f(double e, double v) {
        double r1201228 = v;
        double r1201229 = sin(r1201228);
        double r1201230 = 1.0;
        double r1201231 = cos(r1201228);
        double r1201232 = e;
        double r1201233 = r1201231 * r1201232;
        double r1201234 = r1201230 + r1201233;
        double r1201235 = r1201229 / r1201234;
        double r1201236 = r1201235 * r1201232;
        return r1201236;
}

Error

Bits error versus e

Bits error versus v

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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)))))