Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[e \cdot \frac{\sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
e \cdot \frac{\sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r10689 = e;
        double r10690 = v;
        double r10691 = sin(r10690);
        double r10692 = r10689 * r10691;
        double r10693 = 1.0;
        double r10694 = cos(r10690);
        double r10695 = r10689 * r10694;
        double r10696 = r10693 + r10695;
        double r10697 = r10692 / r10696;
        return r10697;
}
↓
double f(double e, double v) {
        double r10698 = e;
        double r10699 = v;
        double r10700 = sin(r10699);
        double r10701 = 1.0;
        double r10702 = cos(r10699);
        double r10703 = r10698 * r10702;
        double r10704 = r10701 + r10703;
        double r10705 = r10700 / r10704;
        double r10706 = r10698 * r10705;
        return r10706;
}

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 *-un-lft-identity0.1

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))