Average Error: 0.1 → 0.1
Time: 19.6s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(\left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - e \cdot \cos v\right) + 1\right) \cdot \left(\sin v \cdot \frac{e}{\left(e \cdot \cos v\right) \cdot \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)\right) + 1}\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\left(\left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - e \cdot \cos v\right) + 1\right) \cdot \left(\sin v \cdot \frac{e}{\left(e \cdot \cos v\right) \cdot \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)\right) + 1}\right)
double f(double e, double v) {
        double r622252 = e;
        double r622253 = v;
        double r622254 = sin(r622253);
        double r622255 = r622252 * r622254;
        double r622256 = 1.0;
        double r622257 = cos(r622253);
        double r622258 = r622252 * r622257;
        double r622259 = r622256 + r622258;
        double r622260 = r622255 / r622259;
        return r622260;
}
↓
double f(double e, double v) {
        double r622261 = e;
        double r622262 = v;
        double r622263 = cos(r622262);
        double r622264 = r622261 * r622263;
        double r622265 = r622264 * r622264;
        double r622266 = r622265 - r622264;
        double r622267 = 1.0;
        double r622268 = r622266 + r622267;
        double r622269 = sin(r622262);
        double r622270 = r622264 * r622265;
        double r622271 = r622270 + r622267;
        double r622272 = r622261 / r622271;
        double r622273 = r622269 * r622272;
        double r622274 = r622268 * r622273;
        return r622274;
}

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 flip3-+0.1

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

  4. Applied associate-/r/0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019129 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))