Average Error: 0.1 → 0.1
Time: 20.9s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\left(\frac{e}{1 - \left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)} \cdot \sin v\right) \cdot \left(1 - \cos v \cdot e\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\left(\frac{e}{1 - \left(\cos v \cdot e\right) \cdot \left(\cos v \cdot e\right)} \cdot \sin v\right) \cdot \left(1 - \cos v \cdot e\right)
double f(double e, double v) {
        double r476048 = e;
        double r476049 = v;
        double r476050 = sin(r476049);
        double r476051 = r476048 * r476050;
        double r476052 = 1.0;
        double r476053 = cos(r476049);
        double r476054 = r476048 * r476053;
        double r476055 = r476052 + r476054;
        double r476056 = r476051 / r476055;
        return r476056;
}
↓
double f(double e, double v) {
        double r476057 = e;
        double r476058 = 1.0;
        double r476059 = v;
        double r476060 = cos(r476059);
        double r476061 = r476060 * r476057;
        double r476062 = r476061 * r476061;
        double r476063 = r476058 - r476062;
        double r476064 = r476057 / r476063;
        double r476065 = sin(r476059);
        double r476066 = r476064 * r476065;
        double r476067 = r476058 - r476061;
        double r476068 = r476066 * r476067;
        return r476068;
}

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 flip-+0.1

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

  4. Applied associate-/r/0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019153 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))