Average Error: 15.1 → 14.6
Time: 5.5s
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 r262308 = 1.0;
        double r262309 = 0.5;
        double r262310 = x;
        double r262311 = hypot(r262308, r262310);
        double r262312 = r262308 / r262311;
        double r262313 = r262308 + r262312;
        double r262314 = r262309 * r262313;
        double r262315 = sqrt(r262314);
        double r262316 = r262308 - r262315;
        return r262316;
}
↓
double f(double x) {
        double r262317 = 1.0;
        double r262318 = r262317 * r262317;
        double r262319 = 0.5;
        double r262320 = x;
        double r262321 = hypot(r262317, r262320);
        double r262322 = r262317 / r262321;
        double r262323 = r262317 + r262322;
        double r262324 = r262319 * r262323;
        double r262325 = sqrt(r262324);
        double r262326 = r262325 * r262325;
        double r262327 = r262317 * r262325;
        double r262328 = r262326 - r262327;
        double r262329 = r262318 + r262328;
        double r262330 = 3.0;
        double r262331 = pow(r262317, r262330);
        double r262332 = r262331 * r262331;
        double r262333 = pow(r262325, r262330);
        double r262334 = r262333 * r262333;
        double r262335 = r262331 * r262333;
        double r262336 = r262334 - r262335;
        double r262337 = r262332 + r262336;
        double r262338 = r262317 - r262319;
        double r262339 = r262317 * r262338;
        double r262340 = pow(r262331, r262330);
        double r262341 = pow(r262333, r262330);
        double r262342 = r262340 + r262341;
        double r262343 = r262339 / r262342;
        double r262344 = r262319 * r262322;
        double r262345 = r262344 / r262342;
        double r262346 = r262343 - r262345;
        double r262347 = r262337 * r262346;
        double r262348 = r262329 * r262347;
        return r262348;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

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

  3. Applied flip--15.1

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

  4. Simplified14.6

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

  6. Applied div-sub14.6

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

  8. Applied flip3-+14.6

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

  9. Applied associate-/r/14.6

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

  10. Applied flip3-+15.1

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

  11. Applied associate-/r/14.7

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

  12. Applied distribute-rgt-out--14.6

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

  14. Applied flip3-+14.7

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

  15. Applied associate-/r/14.6

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

  16. Applied flip3-+14.6

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

  17. Applied associate-/r/14.7

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

  18. Applied distribute-rgt-out--14.6

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

  19. Final simplification14.6

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  :precision binary64
  (- 1 (sqrt (* 0.5 (+ 1 (/ 1 (hypot 1 x)))))))