Average Error: 0.1 → 0.1
Time: 20.6s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{{1}^{3} + {\left(e \cdot \cos v\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - 1 \cdot \left(e \cdot \cos v\right)\right)\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\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)
double f(double e, double v) {
        double r22649 = e;
        double r22650 = v;
        double r22651 = sin(r22650);
        double r22652 = r22649 * r22651;
        double r22653 = 1.0;
        double r22654 = cos(r22650);
        double r22655 = r22649 * r22654;
        double r22656 = r22653 + r22655;
        double r22657 = r22652 / r22656;
        return r22657;
}
↓
double f(double e, double v) {
        double r22658 = e;
        double r22659 = v;
        double r22660 = sin(r22659);
        double r22661 = r22658 * r22660;
        double r22662 = 1.0;
        double r22663 = 3.0;
        double r22664 = pow(r22662, r22663);
        double r22665 = cos(r22659);
        double r22666 = r22658 * r22665;
        double r22667 = pow(r22666, r22663);
        double r22668 = r22664 + r22667;
        double r22669 = r22661 / r22668;
        double r22670 = r22662 * r22662;
        double r22671 = r22666 * r22666;
        double r22672 = r22662 * r22666;
        double r22673 = r22671 - r22672;
        double r22674 = r22670 + r22673;
        double r22675 = r22669 * r22674;
        return r22675;
}

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. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{{1}^{3} + {\left(e \cdot \cos v\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(e \cdot \cos v\right) \cdot \left(e \cdot \cos v\right) - 1 \cdot \left(e \cdot \cos v\right)\right)\right)\]

Reproduce

herbie shell --seed 2019306 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))