Average Error: 0.1 → 0.1
Time: 19.0s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(\frac{\sin v}{1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot e\right) \cdot \left(1 - e \cdot \cos v\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\left(\frac{\sin v}{1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot e\right) \cdot \left(1 - e \cdot \cos v\right)
double f(double e, double v) {
        double r595247 = e;
        double r595248 = v;
        double r595249 = sin(r595248);
        double r595250 = r595247 * r595249;
        double r595251 = 1.0;
        double r595252 = cos(r595248);
        double r595253 = r595247 * r595252;
        double r595254 = r595251 + r595253;
        double r595255 = r595250 / r595254;
        return r595255;
}
↓
double f(double e, double v) {
        double r595256 = v;
        double r595257 = sin(r595256);
        double r595258 = 1.0;
        double r595259 = e;
        double r595260 = cos(r595256);
        double r595261 = r595259 * r595260;
        double r595262 = r595261 * r595261;
        double r595263 = r595258 - r595262;
        double r595264 = r595257 / r595263;
        double r595265 = r595264 * r595259;
        double r595266 = r595258 - r595261;
        double r595267 = r595265 * r595266;
        return r595267;
}

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 flip-+0.1

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

  4. Applied associate-/r/0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019134 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))