Average Error: 0.1 → 0.1
Time: 34.7s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(\sin v \cdot \frac{e}{\left(\left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)\right) \cdot \left(\cos v \cdot e\right) + \left(1 \cdot 1\right) \cdot 1}\right) \cdot \left(\left(\left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right) - \left(\cos v \cdot e\right) \cdot 1\right) + 1 \cdot 1\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\left(\sin v \cdot \frac{e}{\left(\left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)\right) \cdot \left(\cos v \cdot e\right) + \left(1 \cdot 1\right) \cdot 1}\right) \cdot \left(\left(\left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right) - \left(\cos v \cdot e\right) \cdot 1\right) + 1 \cdot 1\right)
double f(double e, double v) {
        double r1087983 = e;
        double r1087984 = v;
        double r1087985 = sin(r1087984);
        double r1087986 = r1087983 * r1087985;
        double r1087987 = 1.0;
        double r1087988 = cos(r1087984);
        double r1087989 = r1087983 * r1087988;
        double r1087990 = r1087987 + r1087989;
        double r1087991 = r1087986 / r1087990;
        return r1087991;
}
↓
double f(double e, double v) {
        double r1087992 = v;
        double r1087993 = sin(r1087992);
        double r1087994 = e;
        double r1087995 = cos(r1087992);
        double r1087996 = r1087995 * r1087994;
        double r1087997 = r1087996 * r1087996;
        double r1087998 = r1087997 * r1087996;
        double r1087999 = 1.0;
        double r1088000 = r1087999 * r1087999;
        double r1088001 = r1088000 * r1087999;
        double r1088002 = r1087998 + r1088001;
        double r1088003 = r1087994 / r1088002;
        double r1088004 = r1087993 * r1088003;
        double r1088005 = r1087996 * r1087999;
        double r1088006 = r1087997 - r1088005;
        double r1088007 = r1088006 + r1088000;
        double r1088008 = r1088004 * r1088007;
        return r1088008;
}

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

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))