Average Error: 0.1 → 0.1
Time: 9.0s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r18323 = e;
        double r18324 = v;
        double r18325 = sin(r18324);
        double r18326 = r18323 * r18325;
        double r18327 = 1.0;
        double r18328 = cos(r18324);
        double r18329 = r18323 * r18328;
        double r18330 = r18327 + r18329;
        double r18331 = r18326 / r18330;
        return r18331;
}
↓
double f(double e, double v) {
        double r18332 = e;
        double r18333 = v;
        double r18334 = sin(r18333);
        double r18335 = r18332 * r18334;
        double r18336 = 1.0;
        double r18337 = cos(r18333);
        double r18338 = r18332 * r18337;
        double r18339 = r18336 + r18338;
        double r18340 = r18335 / r18339;
        return r18340;
}

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

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

Reproduce

herbie shell --seed 2019308 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))