Average Error: 0.4 → 0.3
Time: 21.9s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{t} \cdot \frac{\frac{1}{\pi}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
\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{1 - 5 \cdot \left(v \cdot v\right)}{t} \cdot \frac{\frac{1}{\pi}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r227606 = 1.0;
        double r227607 = 5.0;
        double r227608 = v;
        double r227609 = r227608 * r227608;
        double r227610 = r227607 * r227609;
        double r227611 = r227606 - r227610;
        double r227612 = atan2(1.0, 0.0);
        double r227613 = t;
        double r227614 = r227612 * r227613;
        double r227615 = 2.0;
        double r227616 = 3.0;
        double r227617 = r227616 * r227609;
        double r227618 = r227606 - r227617;
        double r227619 = r227615 * r227618;
        double r227620 = sqrt(r227619);
        double r227621 = r227614 * r227620;
        double r227622 = r227606 - r227609;
        double r227623 = r227621 * r227622;
        double r227624 = r227611 / r227623;
        return r227624;
}
↓
double f(double v, double t) {
        double r227625 = 1.0;
        double r227626 = 5.0;
        double r227627 = v;
        double r227628 = r227627 * r227627;
        double r227629 = r227626 * r227628;
        double r227630 = r227625 - r227629;
        double r227631 = t;
        double r227632 = r227630 / r227631;
        double r227633 = 1.0;
        double r227634 = atan2(1.0, 0.0);
        double r227635 = r227633 / r227634;
        double r227636 = 2.0;
        double r227637 = 3.0;
        double r227638 = r227637 * r227628;
        double r227639 = r227625 - r227638;
        double r227640 = r227636 * r227639;
        double r227641 = sqrt(r227640);
        double r227642 = r227635 / r227641;
        double r227643 = r227632 * r227642;
        double r227644 = r227625 - r227628;
        double r227645 = r227643 / r227644;
        return r227645;
}

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 associate-/r*0.4

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

  5. Applied associate-*l*0.4

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

  7. Applied associate-/r*0.3

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

  9. Applied div-inv0.3

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

  10. Applied times-frac0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))