Average Error: 0.1 → 0.1
Time: 25.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v \cdot e}{\left(e \cdot \cos v\right) \cdot \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right)\right) + 1 \cdot \left(1 \cdot 1\right)} \cdot \left(1 \cdot 1 + \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - 1 \cdot \left(e \cdot \cos v\right)\right)\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v \cdot 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 \left(1 \cdot 1\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)
double f(double e, double v) {
        double r2557803 = e;
        double r2557804 = v;
        double r2557805 = sin(r2557804);
        double r2557806 = r2557803 * r2557805;
        double r2557807 = 1.0;
        double r2557808 = cos(r2557804);
        double r2557809 = r2557803 * r2557808;
        double r2557810 = r2557807 + r2557809;
        double r2557811 = r2557806 / r2557810;
        return r2557811;
}
↓
double f(double e, double v) {
        double r2557812 = v;
        double r2557813 = sin(r2557812);
        double r2557814 = e;
        double r2557815 = r2557813 * r2557814;
        double r2557816 = cos(r2557812);
        double r2557817 = r2557814 * r2557816;
        double r2557818 = r2557817 * r2557817;
        double r2557819 = r2557817 * r2557818;
        double r2557820 = 1.0;
        double r2557821 = r2557820 * r2557820;
        double r2557822 = r2557820 * r2557821;
        double r2557823 = r2557819 + r2557822;
        double r2557824 = r2557815 / r2557823;
        double r2557825 = r2557820 * r2557817;
        double r2557826 = r2557818 - r2557825;
        double r2557827 = r2557821 + r2557826;
        double r2557828 = r2557824 * r2557827;
        return r2557828;
}

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

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))