Average Error: 0.1 → 0.1
Time: 5.2s
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 r13818 = e;
        double r13819 = v;
        double r13820 = sin(r13819);
        double r13821 = r13818 * r13820;
        double r13822 = 1.0;
        double r13823 = cos(r13819);
        double r13824 = r13818 * r13823;
        double r13825 = r13822 + r13824;
        double r13826 = r13821 / r13825;
        return r13826;
}
↓
double f(double e, double v) {
        double r13827 = e;
        double r13828 = v;
        double r13829 = sin(r13828);
        double r13830 = 1.0;
        double r13831 = cos(r13828);
        double r13832 = r13827 * r13831;
        double r13833 = r13830 + r13832;
        double r13834 = r13829 / r13833;
        double r13835 = r13827 * r13834;
        return r13835;
}

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

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

Reproduce

herbie shell --seed 2020018 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))