Average Error: 0.4 → 0.4
Time: 37.1s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 \cdot 1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}\right) \cdot \left(1 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(\sqrt{1 + 3 \cdot \left(v \cdot v\right)} \cdot \left(1 + v \cdot v\right)\right)\]
\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{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 \cdot 1 - \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)} \cdot \left(\sqrt{1 + 3 \cdot \left(v \cdot v\right)} \cdot \left(1 + v \cdot v\right)\right)
double f(double v, double t) {
        double r9476616 = 1.0;
        double r9476617 = 5.0;
        double r9476618 = v;
        double r9476619 = r9476618 * r9476618;
        double r9476620 = r9476617 * r9476619;
        double r9476621 = r9476616 - r9476620;
        double r9476622 = atan2(1.0, 0.0);
        double r9476623 = t;
        double r9476624 = r9476622 * r9476623;
        double r9476625 = 2.0;
        double r9476626 = 3.0;
        double r9476627 = r9476626 * r9476619;
        double r9476628 = r9476616 - r9476627;
        double r9476629 = r9476625 * r9476628;
        double r9476630 = sqrt(r9476629);
        double r9476631 = r9476624 * r9476630;
        double r9476632 = r9476616 - r9476619;
        double r9476633 = r9476631 * r9476632;
        double r9476634 = r9476621 / r9476633;
        return r9476634;
}
↓
double f(double v, double t) {
        double r9476635 = 1.0;
        double r9476636 = 5.0;
        double r9476637 = v;
        double r9476638 = r9476637 * r9476637;
        double r9476639 = r9476636 * r9476638;
        double r9476640 = r9476635 - r9476639;
        double r9476641 = atan2(1.0, 0.0);
        double r9476642 = t;
        double r9476643 = r9476641 * r9476642;
        double r9476644 = 2.0;
        double r9476645 = r9476635 * r9476635;
        double r9476646 = 3.0;
        double r9476647 = r9476646 * r9476638;
        double r9476648 = r9476647 * r9476647;
        double r9476649 = r9476645 - r9476648;
        double r9476650 = r9476644 * r9476649;
        double r9476651 = sqrt(r9476650);
        double r9476652 = r9476643 * r9476651;
        double r9476653 = r9476638 * r9476638;
        double r9476654 = r9476645 - r9476653;
        double r9476655 = r9476652 * r9476654;
        double r9476656 = r9476640 / r9476655;
        double r9476657 = r9476635 + r9476647;
        double r9476658 = sqrt(r9476657);
        double r9476659 = r9476635 + r9476638;
        double r9476660 = r9476658 * r9476659;
        double r9476661 = r9476656 * r9476660;
        return r9476661;
}

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 flip--0.4

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

  4. Applied flip--0.4

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

  5. Applied associate-*r/0.4

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

  6. Applied sqrt-div0.5

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

  7. Applied associate-*r/0.5

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

  8. Applied frac-times0.5

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

  9. Applied associate-/r/0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))))