Average Error: 0.1 → 0.1
Time: 18.5s
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 r462566 = e;
        double r462567 = v;
        double r462568 = sin(r462567);
        double r462569 = r462566 * r462568;
        double r462570 = 1.0;
        double r462571 = cos(r462567);
        double r462572 = r462566 * r462571;
        double r462573 = r462570 + r462572;
        double r462574 = r462569 / r462573;
        return r462574;
}
↓
double f(double e, double v) {
        double r462575 = e;
        double r462576 = 1.0;
        double r462577 = v;
        double r462578 = cos(r462577);
        double r462579 = r462578 * r462575;
        double r462580 = r462579 * r462579;
        double r462581 = r462576 - r462580;
        double r462582 = r462575 / r462581;
        double r462583 = sin(r462577);
        double r462584 = r462582 * r462583;
        double r462585 = r462576 - r462579;
        double r462586 = r462584 * r462585;
        return r462586;
}

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)))))