Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v}{1 + \cos v \cdot e} \cdot e\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v}{1 + \cos v \cdot e} \cdot e
double f(double e, double v) {
        double r846757 = e;
        double r846758 = v;
        double r846759 = sin(r846758);
        double r846760 = r846757 * r846759;
        double r846761 = 1.0;
        double r846762 = cos(r846758);
        double r846763 = r846757 * r846762;
        double r846764 = r846761 + r846763;
        double r846765 = r846760 / r846764;
        return r846765;
}
↓
double f(double e, double v) {
        double r846766 = v;
        double r846767 = sin(r846766);
        double r846768 = 1.0;
        double r846769 = cos(r846766);
        double r846770 = e;
        double r846771 = r846769 * r846770;
        double r846772 = r846768 + r846771;
        double r846773 = r846767 / r846772;
        double r846774 = r846773 * r846770;
        return r846774;
}

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 *-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

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

Reproduce

herbie shell --seed 2019170 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))