Average Error: 0.1 → 0.1
Time: 21.4s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\sin v \cdot \frac{e}{1 + \cos v \cdot e}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\sin v \cdot \frac{e}{1 + \cos v \cdot e}
double f(double e, double v) {
        double r994817 = e;
        double r994818 = v;
        double r994819 = sin(r994818);
        double r994820 = r994817 * r994819;
        double r994821 = 1.0;
        double r994822 = cos(r994818);
        double r994823 = r994817 * r994822;
        double r994824 = r994821 + r994823;
        double r994825 = r994820 / r994824;
        return r994825;
}
↓
double f(double e, double v) {
        double r994826 = v;
        double r994827 = sin(r994826);
        double r994828 = e;
        double r994829 = 1.0;
        double r994830 = cos(r994826);
        double r994831 = r994830 * r994828;
        double r994832 = r994829 + r994831;
        double r994833 = r994828 / r994832;
        double r994834 = r994827 * r994833;
        return r994834;
}

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 add-sqr-sqrt0.1

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

  4. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{e \cdot \sin v}{\sqrt{1 + e \cdot \cos v}}}{\sqrt{1 + e \cdot \cos v}}}\]
  5. Using strategy rm

  6. Applied *-commutative0.1

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

  7. Applied associate-/l*0.3

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

  8. Applied associate-/l/0.3

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

  9. Simplified0.3

    \[\leadsto \frac{\sin v}{\color{blue}{\frac{\cos v \cdot e + 1}{e}}}\]
  10. Using strategy rm

  11. Applied div-inv0.2

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))