Average Error: 0.4 → 0.1
Time: 27.5s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(5 \cdot v\right) \cdot v}{\pi}}{\sqrt{\left(1 \cdot 1 - \left(\left(3 \cdot v\right) \cdot v\right) \cdot \left(\left(3 \cdot v\right) \cdot v\right)\right) \cdot 2}}}{t}}{\left(1 \cdot 1\right) \cdot 1 - \left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(\left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(v \cdot v\right) \cdot 1\right) + 1 \cdot 1\right) \cdot \sqrt{1 + 3 \cdot \left(v \cdot v\right)}\right)\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{\frac{\frac{\frac{1 - \left(5 \cdot v\right) \cdot v}{\pi}}{\sqrt{\left(1 \cdot 1 - \left(\left(3 \cdot v\right) \cdot v\right) \cdot \left(\left(3 \cdot v\right) \cdot v\right)\right) \cdot 2}}}{t}}{\left(1 \cdot 1\right) \cdot 1 - \left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(\left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(v \cdot v\right) \cdot 1\right) + 1 \cdot 1\right) \cdot \sqrt{1 + 3 \cdot \left(v \cdot v\right)}\right)
double f(double v, double t) {
        double r7700605 = 1.0;
        double r7700606 = 5.0;
        double r7700607 = v;
        double r7700608 = r7700607 * r7700607;
        double r7700609 = r7700606 * r7700608;
        double r7700610 = r7700605 - r7700609;
        double r7700611 = atan2(1.0, 0.0);
        double r7700612 = t;
        double r7700613 = r7700611 * r7700612;
        double r7700614 = 2.0;
        double r7700615 = 3.0;
        double r7700616 = r7700615 * r7700608;
        double r7700617 = r7700605 - r7700616;
        double r7700618 = r7700614 * r7700617;
        double r7700619 = sqrt(r7700618);
        double r7700620 = r7700613 * r7700619;
        double r7700621 = r7700605 - r7700608;
        double r7700622 = r7700620 * r7700621;
        double r7700623 = r7700610 / r7700622;
        return r7700623;
}
↓
double f(double v, double t) {
        double r7700624 = 1.0;
        double r7700625 = 5.0;
        double r7700626 = v;
        double r7700627 = r7700625 * r7700626;
        double r7700628 = r7700627 * r7700626;
        double r7700629 = r7700624 - r7700628;
        double r7700630 = atan2(1.0, 0.0);
        double r7700631 = r7700629 / r7700630;
        double r7700632 = r7700624 * r7700624;
        double r7700633 = 3.0;
        double r7700634 = r7700633 * r7700626;
        double r7700635 = r7700634 * r7700626;
        double r7700636 = r7700635 * r7700635;
        double r7700637 = r7700632 - r7700636;
        double r7700638 = 2.0;
        double r7700639 = r7700637 * r7700638;
        double r7700640 = sqrt(r7700639);
        double r7700641 = r7700631 / r7700640;
        double r7700642 = t;
        double r7700643 = r7700641 / r7700642;
        double r7700644 = r7700632 * r7700624;
        double r7700645 = r7700626 * r7700626;
        double r7700646 = r7700645 * r7700645;
        double r7700647 = r7700645 * r7700646;
        double r7700648 = r7700644 - r7700647;
        double r7700649 = r7700643 / r7700648;
        double r7700650 = r7700645 * r7700624;
        double r7700651 = r7700646 + r7700650;
        double r7700652 = r7700651 + r7700632;
        double r7700653 = r7700633 * r7700645;
        double r7700654 = r7700624 + r7700653;
        double r7700655 = sqrt(r7700654);
        double r7700656 = r7700652 * r7700655;
        double r7700657 = r7700649 * r7700656;
        return r7700657;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
  2. Using strategy rm

  3. Applied flip3--0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \color{blue}{\frac{{1}^{3} - {\left(v \cdot v\right)}^{3}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}}\]

  4. Applied flip--0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \color{blue}{\frac{1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)}{1 + 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \frac{{1}^{3} - {\left(v \cdot v\right)}^{3}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}\]

  5. Applied associate-*r/0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{\color{blue}{\frac{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}{1 + 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \frac{{1}^{3} - {\left(v \cdot v\right)}^{3}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}\]

  6. Applied sqrt-div0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \color{blue}{\frac{\sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \frac{{1}^{3} - {\left(v \cdot v\right)}^{3}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}\]

  7. Applied associate-*r/0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\frac{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)}}} \cdot \frac{{1}^{3} - {\left(v \cdot v\right)}^{3}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}\]

  8. Applied frac-times0.4

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\frac{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}\right) \cdot \left({1}^{3} - {\left(v \cdot v\right)}^{3}\right)}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)} \cdot \left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)\right)}}}\]

  9. Applied associate-/r/0.4

    \[\leadsto \color{blue}{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}\right) \cdot \left({1}^{3} - {\left(v \cdot v\right)}^{3}\right)} \cdot \left(\sqrt{1 + 3 \cdot \left(v \cdot v\right)} \cdot \left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)\right)\right)}\]

  10. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - v \cdot \left(5 \cdot v\right)}{\pi}}{\sqrt{2 \cdot \left(1 \cdot 1 - \left(\left(3 \cdot v\right) \cdot v\right) \cdot \left(\left(3 \cdot v\right) \cdot v\right)\right)} \cdot t}}{\left(1 \cdot 1\right) \cdot 1 - \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)}} \cdot \left(\sqrt{1 + 3 \cdot \left(v \cdot v\right)} \cdot \left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)\right)\right)\]
  11. Using strategy rm

  12. Applied associate-/r*0.1

    \[\leadsto \frac{\color{blue}{\frac{\frac{\frac{1 - v \cdot \left(5 \cdot v\right)}{\pi}}{\sqrt{2 \cdot \left(1 \cdot 1 - \left(\left(3 \cdot v\right) \cdot v\right) \cdot \left(\left(3 \cdot v\right) \cdot v\right)\right)}}}{t}}}{\left(1 \cdot 1\right) \cdot 1 - \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)} \cdot \left(\sqrt{1 + 3 \cdot \left(v \cdot v\right)} \cdot \left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)\right)\right)\]

  13. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{\frac{1 - \left(5 \cdot v\right) \cdot v}{\pi}}{\sqrt{\left(1 \cdot 1 - \left(\left(3 \cdot v\right) \cdot v\right) \cdot \left(\left(3 \cdot v\right) \cdot v\right)\right) \cdot 2}}}{t}}{\left(1 \cdot 1\right) \cdot 1 - \left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(\left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + \left(v \cdot v\right) \cdot 1\right) + 1 \cdot 1\right) \cdot \sqrt{1 + 3 \cdot \left(v \cdot v\right)}\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))