Average Error: 15.6 → 15.1
Time: 5.7s
Precision: 64
\[1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\]
↓
\[\left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}}\right)\right)\]
1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}
↓
\left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}}\right)\right)
double f(double x) {
        double r202562 = 1.0;
        double r202563 = 0.5;
        double r202564 = x;
        double r202565 = hypot(r202562, r202564);
        double r202566 = r202562 / r202565;
        double r202567 = r202562 + r202566;
        double r202568 = r202563 * r202567;
        double r202569 = sqrt(r202568);
        double r202570 = r202562 - r202569;
        return r202570;
}
↓
double f(double x) {
        double r202571 = 1.0;
        double r202572 = r202571 * r202571;
        double r202573 = 0.5;
        double r202574 = x;
        double r202575 = hypot(r202571, r202574);
        double r202576 = r202571 / r202575;
        double r202577 = r202571 + r202576;
        double r202578 = r202573 * r202577;
        double r202579 = sqrt(r202578);
        double r202580 = r202579 * r202579;
        double r202581 = r202571 * r202579;
        double r202582 = r202580 - r202581;
        double r202583 = r202572 + r202582;
        double r202584 = 3.0;
        double r202585 = pow(r202571, r202584);
        double r202586 = r202585 * r202585;
        double r202587 = pow(r202579, r202584);
        double r202588 = r202587 * r202587;
        double r202589 = r202585 * r202587;
        double r202590 = r202588 - r202589;
        double r202591 = r202586 + r202590;
        double r202592 = r202571 - r202573;
        double r202593 = r202571 * r202592;
        double r202594 = pow(r202585, r202584);
        double r202595 = pow(r202587, r202584);
        double r202596 = r202594 + r202595;
        double r202597 = r202593 / r202596;
        double r202598 = r202573 * r202576;
        double r202599 = r202598 / r202596;
        double r202600 = r202597 - r202599;
        double r202601 = r202591 * r202600;
        double r202602 = r202583 * r202601;
        return r202602;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

    \[1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\]
  2. Using strategy rm

  3. Applied flip--15.6

    \[\leadsto \color{blue}{\frac{1 \cdot 1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}}\]

  4. Simplified15.1

    \[\leadsto \frac{\color{blue}{1 \cdot \left(1 - 0.5\right) - 0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}\]
  5. Using strategy rm

  6. Applied div-sub15.1

    \[\leadsto \color{blue}{\frac{1 \cdot \left(1 - 0.5\right)}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}}\]
  7. Using strategy rm

  8. Applied flip3-+15.1

    \[\leadsto \frac{1 \cdot \left(1 - 0.5\right)}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{\color{blue}{\frac{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}}\]

  9. Applied associate-/r/15.1

    \[\leadsto \frac{1 \cdot \left(1 - 0.5\right)}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}} - \color{blue}{\frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)}\]

  10. Applied flip3-+15.6

    \[\leadsto \frac{1 \cdot \left(1 - 0.5\right)}{\color{blue}{\frac{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}}{1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)\]

  11. Applied associate-/r/15.1

    \[\leadsto \color{blue}{\frac{1 \cdot \left(1 - 0.5\right)}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right)\]

  12. Applied distribute-rgt-out--15.1

    \[\leadsto \color{blue}{\left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}}\right)}\]
  13. Using strategy rm

  14. Applied flip3-+15.1

    \[\leadsto \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{\color{blue}{\frac{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}}{{1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}}}\right)\]

  15. Applied associate-/r/15.1

    \[\leadsto \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{1}^{3} + {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}} - \color{blue}{\frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} \cdot \left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right)}\right)\]

  16. Applied flip3-+15.1

    \[\leadsto \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{\color{blue}{\frac{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}}{{1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} \cdot \left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right)\right)\]

  17. Applied associate-/r/15.1

    \[\leadsto \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\color{blue}{\frac{1 \cdot \left(1 - 0.5\right)}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} \cdot \left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right)} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} \cdot \left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right)\right)\]

  18. Applied distribute-rgt-out--15.1

    \[\leadsto \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \color{blue}{\left(\left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}}\right)\right)}\]

  19. Final simplification15.1

    \[\leadsto \left(1 \cdot 1 + \left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)} - 1 \cdot \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)\right) \cdot \left(\left({1}^{3} \cdot {1}^{3} + \left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3} - {1}^{3} \cdot {\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)\right) \cdot \left(\frac{1 \cdot \left(1 - 0.5\right)}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}} - \frac{0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}}{{\left({1}^{3}\right)}^{3} + {\left({\left(\sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\right)}^{3}\right)}^{3}}\right)\right)\]

Reproduce

herbie shell --seed 2020021 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  :precision binary64
  (- 1 (sqrt (* 0.5 (+ 1 (/ 1 (hypot 1 x)))))))