Rosa's FloatVsDoubleBenchmark

Average Error: 0.5 → 0.5

Time: 35.2s

Precision: 64

Math

\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

↓

\[x1 + \left(\left(\left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, -3\right) + \left(3 + \left(-3\right)\right), \frac{\left(\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot 4\right) \cdot \left(x1 \cdot x1\right)\right) + \left(-\left(x1 \cdot x1\right) \cdot 6\right)\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + x1\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right)\]

C

double f(double x1, double x2) {
        double r80203 = x1;
        double r80204 = 2.0;
        double r80205 = r80204 * r80203;
        double r80206 = 3.0;
        double r80207 = r80206 * r80203;
        double r80208 = r80207 * r80203;
        double r80209 = x2;
        double r80210 = r80204 * r80209;
        double r80211 = r80208 + r80210;
        double r80212 = r80211 - r80203;
        double r80213 = r80203 * r80203;
        double r80214 = 1.0;
        double r80215 = r80213 + r80214;
        double r80216 = r80212 / r80215;
        double r80217 = r80205 * r80216;
        double r80218 = r80216 - r80206;
        double r80219 = r80217 * r80218;
        double r80220 = 4.0;
        double r80221 = r80220 * r80216;
        double r80222 = 6.0;
        double r80223 = r80221 - r80222;
        double r80224 = r80213 * r80223;
        double r80225 = r80219 + r80224;
        double r80226 = r80225 * r80215;
        double r80227 = r80208 * r80216;
        double r80228 = r80226 + r80227;
        double r80229 = r80213 * r80203;
        double r80230 = r80228 + r80229;
        double r80231 = r80230 + r80203;
        double r80232 = r80208 - r80210;
        double r80233 = r80232 - r80203;
        double r80234 = r80233 / r80215;
        double r80235 = r80206 * r80234;
        double r80236 = r80231 + r80235;
        double r80237 = r80203 + r80236;
        return r80237;
}

↓

double f(double x1, double x2) {
        double r80238 = x1;
        double r80239 = 1.0;
        double r80240 = r80238 * r80238;
        double r80241 = r80239 + r80240;
        double r80242 = 1.0;
        double r80243 = fma(r80238, r80238, r80239);
        double r80244 = sqrt(r80243);
        double r80245 = r80242 / r80244;
        double r80246 = 3.0;
        double r80247 = r80238 * r80246;
        double r80248 = x2;
        double r80249 = 2.0;
        double r80250 = r80248 * r80249;
        double r80251 = fma(r80238, r80247, r80250);
        double r80252 = r80251 - r80238;
        double r80253 = r80252 / r80244;
        double r80254 = -r80246;
        double r80255 = fma(r80245, r80253, r80254);
        double r80256 = r80246 + r80254;
        double r80257 = r80255 + r80256;
        double r80258 = fma(r80247, r80238, r80250);
        double r80259 = r80258 - r80238;
        double r80260 = r80238 * r80249;
        double r80261 = r80259 * r80260;
        double r80262 = r80261 / r80243;
        double r80263 = r80259 / r80243;
        double r80264 = 4.0;
        double r80265 = r80263 * r80264;
        double r80266 = r80265 * r80240;
        double r80267 = fma(r80257, r80262, r80266);
        double r80268 = 6.0;
        double r80269 = r80240 * r80268;
        double r80270 = -r80269;
        double r80271 = r80267 + r80270;
        double r80272 = r80241 * r80271;
        double r80273 = r80238 * r80247;
        double r80274 = r80273 + r80250;
        double r80275 = r80274 - r80238;
        double r80276 = r80275 / r80241;
        double r80277 = r80276 * r80273;
        double r80278 = r80272 + r80277;
        double r80279 = r80238 * r80240;
        double r80280 = r80278 + r80279;
        double r80281 = r80280 + r80238;
        double r80282 = r80273 - r80250;
        double r80283 = r80282 - r80238;
        double r80284 = r80283 / r80241;
        double r80285 = r80284 * r80246;
        double r80286 = r80281 + r80285;
        double r80287 = r80238 + r80286;
        return r80287;
}

Error

Bits error versus x1

Bits error versus x2

Derivation

1. Initial program 0.5

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
2. Using strategy rm

3. Applied sub-neg 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \color{blue}{\left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(-6\right)\right)}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

4. Applied distribute-lft-in 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{\left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right)}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

5. Applied associate-+r+ 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

6. Simplified 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - 3, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)} + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
7. Using strategy rm

8. Applied add-cube-cbrt 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} - \color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

9. Applied add-sqr-sqrt 0.5

   \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\color{blue}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}} - \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

10. Applied *-un-lft-identity 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\frac{\color{blue}{1 \cdot \left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right)}}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \sqrt{\mathsf{fma}\left(x1, x1, 1\right)}} - \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

11. Applied times-frac 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\color{blue}{\frac{1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}} \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}} - \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

12. Applied prod-diff 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, -\sqrt[3]{3} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{3}, \sqrt[3]{3} \cdot \sqrt[3]{3}, \sqrt[3]{3} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right)}, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

13. Simplified 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, -3\right)} + \mathsf{fma}\left(-\sqrt[3]{3}, \sqrt[3]{3} \cdot \sqrt[3]{3}, \sqrt[3]{3} \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right), \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

14. Simplified 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right) - x1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, -3\right) + \color{blue}{\left(\left(-3\right) + 3\right)}, \frac{\left(\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\mathsf{fma}\left(3 \cdot x1, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + \left(x1 \cdot x1\right) \cdot \left(-6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

15. Final simplification 0.5

    \[\leadsto x1 + \left(\left(\left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\sqrt{\mathsf{fma}\left(x1, x1, 1\right)}}, -3\right) + \left(3 + \left(-3\right)\right), \frac{\left(\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1\right) \cdot \left(x1 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot 4\right) \cdot \left(x1 \cdot x1\right)\right) + \left(-\left(x1 \cdot x1\right) \cdot 6\right)\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + x1\right) + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} \cdot 3\right)\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))