Average Error: 0.1 → 0.1
Time: 42.0s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 \cdot 1 - \left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)} \cdot \left(1 - e \cdot \cos v\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\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)
double f(double e, double v) {
        double r915303 = e;
        double r915304 = v;
        double r915305 = sin(r915304);
        double r915306 = r915303 * r915305;
        double r915307 = 1.0;
        double r915308 = cos(r915304);
        double r915309 = r915303 * r915308;
        double r915310 = r915307 + r915309;
        double r915311 = r915306 / r915310;
        return r915311;
}
↓
double f(double e, double v) {
        double r915312 = e;
        double r915313 = v;
        double r915314 = sin(r915313);
        double r915315 = r915312 * r915314;
        double r915316 = 1.0;
        double r915317 = r915316 * r915316;
        double r915318 = cos(r915313);
        double r915319 = r915312 * r915318;
        double r915320 = r915319 * r915319;
        double r915321 = r915317 - r915320;
        double r915322 = r915315 / r915321;
        double r915323 = r915316 - r915319;
        double r915324 = r915322 * r915323;
        return r915324;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))