Average Error: 14.8 → 14.3
Time: 7.0s
Precision: 64
\[1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}\]
↓
\[\frac{\frac{{\left(1 \cdot \left(1 - 0.5\right)\right)}^{3} - {\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3}}{\left(\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left({\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3} + {\left(1 \cdot \left(1 - 0.5\right)\right)}^{3}\right)\right) \cdot \left(\left(1 + 0.5\right) \cdot \left(1 \cdot 1 + \left(0.5 \cdot 0.5 + 1 \cdot 0.5\right)\right)\right) + \left(\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + \left(\left(1 \cdot \left(1 - 0.5\right)\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right) - \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right)\right)\right) \cdot \left(\left(1 \cdot \left(1 \cdot 1 - 0.5 \cdot 0.5\right)\right) \cdot \left(1 \cdot \left({1}^{3} - {0.5}^{3}\right)\right)\right)} \cdot \left(\left(\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + \left(\left(1 \cdot \left(1 - 0.5\right)\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right) - \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right)\right)\right) \cdot \left(\left(1 + 0.5\right) \cdot \left(1 \cdot 1 + \left(0.5 \cdot 0.5 + 1 \cdot 0.5\right)\right)\right)\right)}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}\]
1 - \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}
↓
\frac{\frac{{\left(1 \cdot \left(1 - 0.5\right)\right)}^{3} - {\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3}}{\left(\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left({\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}^{3} + {\left(1 \cdot \left(1 - 0.5\right)\right)}^{3}\right)\right) \cdot \left(\left(1 + 0.5\right) \cdot \left(1 \cdot 1 + \left(0.5 \cdot 0.5 + 1 \cdot 0.5\right)\right)\right) + \left(\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + \left(\left(1 \cdot \left(1 - 0.5\right)\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right) - \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right)\right)\right) \cdot \left(\left(1 \cdot \left(1 \cdot 1 - 0.5 \cdot 0.5\right)\right) \cdot \left(1 \cdot \left({1}^{3} - {0.5}^{3}\right)\right)\right)} \cdot \left(\left(\left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) + \left(\left(1 \cdot \left(1 - 0.5\right)\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right) - \left(0.5 \cdot \frac{1}{\mathsf{hypot}\left(1, x\right)}\right) \cdot \left(1 \cdot \left(1 - 0.5\right)\right)\right)\right) \cdot \left(\left(1 + 0.5\right) \cdot \left(1 \cdot 1 + \left(0.5 \cdot 0.5 + 1 \cdot 0.5\right)\right)\right)\right)}{1 + \sqrt{0.5 \cdot \left(1 + \frac{1}{\mathsf{hypot}\left(1, x\right)}\right)}}
double f(double x) {
        double r194204 = 1.0;
        double r194205 = 0.5;
        double r194206 = x;
        double r194207 = hypot(r194204, r194206);
        double r194208 = r194204 / r194207;
        double r194209 = r194204 + r194208;
        double r194210 = r194205 * r194209;
        double r194211 = sqrt(r194210);
        double r194212 = r194204 - r194211;
        return r194212;
}
↓
double f(double x) {
        double r194213 = 1.0;
        double r194214 = 0.5;
        double r194215 = r194213 - r194214;
        double r194216 = r194213 * r194215;
        double r194217 = 3.0;
        double r194218 = pow(r194216, r194217);
        double r194219 = x;
        double r194220 = hypot(r194213, r194219);
        double r194221 = r194213 / r194220;
        double r194222 = r194214 * r194221;
        double r194223 = pow(r194222, r194217);
        double r194224 = r194218 - r194223;
        double r194225 = r194223 + r194218;
        double r194226 = r194222 * r194225;
        double r194227 = r194213 + r194214;
        double r194228 = r194213 * r194213;
        double r194229 = r194214 * r194214;
        double r194230 = r194213 * r194214;
        double r194231 = r194229 + r194230;
        double r194232 = r194228 + r194231;
        double r194233 = r194227 * r194232;
        double r194234 = r194226 * r194233;
        double r194235 = r194222 * r194222;
        double r194236 = r194216 * r194216;
        double r194237 = r194222 * r194216;
        double r194238 = r194236 - r194237;
        double r194239 = r194235 + r194238;
        double r194240 = r194228 - r194229;
        double r194241 = r194213 * r194240;
        double r194242 = pow(r194213, r194217);
        double r194243 = pow(r194214, r194217);
        double r194244 = r194242 - r194243;
        double r194245 = r194213 * r194244;
        double r194246 = r194241 * r194245;
        double r194247 = r194239 * r194246;
        double r194248 = r194234 + r194247;
        double r194249 = r194224 / r194248;
        double r194250 = r194239 * r194233;
        double r194251 = r194249 * r194250;
        double r194252 = r194213 + r194221;
        double r194253 = r194214 * r194252;
        double r194254 = sqrt(r194253);
        double r194255 = r194213 + r194254;
        double r194256 = r194251 / r194255;
        return r194256;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

  3. Applied flip--14.8

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

  4. Simplified14.3

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

  6. Applied flip3--14.3

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

  7. Simplified14.3

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

  9. Applied flip3--14.3

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

  10. Applied associate-*r/14.3

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

  11. Applied flip--14.3

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

  12. Applied associate-*r/14.3

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

  13. Applied frac-times14.3

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

  14. Applied flip3-+14.3

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

  15. Applied associate-*r/14.3

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

  16. Applied frac-add14.3

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

  17. Applied associate-/r/14.3

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

  18. Final simplification14.3

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  :precision binary64
  (- 1 (sqrt (* 0.5 (+ 1 (/ 1 (hypot 1 x)))))))