Jmat.Real.erf

Average Error: 13.9 → 13.1

Time: 46.2s

Precision: 64

Math

\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

↓

\[\frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\frac{\left(1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\frac{1}{\frac{{\left(e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)\right)}^{3}}{{\left(\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}} + \frac{1.421413741000000063863240029604639858007}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right) + \left(0.2548295919999999936678136691625695675611 - \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}}\right)\right) - \frac{0.2844967359999999723108032867457950487733}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}} + {1}^{3}\right)}{\left({\left(\sqrt[3]{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}}\right)}^{6} + 1 \cdot \left(1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)} + 1 \cdot 1}\]

C

double f(double x) {
        double r132214 = 1.0;
        double r132215 = 0.3275911;
        double r132216 = x;
        double r132217 = fabs(r132216);
        double r132218 = r132215 * r132217;
        double r132219 = r132214 + r132218;
        double r132220 = r132214 / r132219;
        double r132221 = 0.254829592;
        double r132222 = -0.284496736;
        double r132223 = 1.421413741;
        double r132224 = -1.453152027;
        double r132225 = 1.061405429;
        double r132226 = r132220 * r132225;
        double r132227 = r132224 + r132226;
        double r132228 = r132220 * r132227;
        double r132229 = r132223 + r132228;
        double r132230 = r132220 * r132229;
        double r132231 = r132222 + r132230;
        double r132232 = r132220 * r132231;
        double r132233 = r132221 + r132232;
        double r132234 = r132220 * r132233;
        double r132235 = r132217 * r132217;
        double r132236 = -r132235;
        double r132237 = exp(r132236);
        double r132238 = r132234 * r132237;
        double r132239 = r132214 - r132238;
        return r132239;
}

↓

double f(double x) {
        double r132240 = 1.0;
        double r132241 = 3.0;
        double r132242 = pow(r132240, r132241);
        double r132243 = 0.254829592;
        double r132244 = 0.3275911;
        double r132245 = x;
        double r132246 = fabs(r132245);
        double r132247 = r132244 * r132246;
        double r132248 = r132240 + r132247;
        double r132249 = r132240 / r132248;
        double r132250 = -0.284496736;
        double r132251 = 1.421413741;
        double r132252 = -1.453152027;
        double r132253 = 1.061405429;
        double r132254 = r132249 * r132253;
        double r132255 = r132252 + r132254;
        double r132256 = r132249 * r132255;
        double r132257 = r132251 + r132256;
        double r132258 = r132249 * r132257;
        double r132259 = r132250 + r132258;
        double r132260 = r132249 * r132259;
        double r132261 = r132243 + r132260;
        double r132262 = 2.0;
        double r132263 = pow(r132246, r132262);
        double r132264 = exp(r132263);
        double r132265 = r132261 / r132264;
        double r132266 = r132240 * r132265;
        double r132267 = r132247 + r132240;
        double r132268 = r132266 / r132267;
        double r132269 = pow(r132268, r132241);
        double r132270 = sqrt(r132269);
        double r132271 = r132270 * r132270;
        double r132272 = r132242 - r132271;
        double r132273 = r132264 * r132267;
        double r132274 = pow(r132273, r132241);
        double r132275 = 4.0;
        double r132276 = pow(r132267, r132275);
        double r132277 = r132253 / r132276;
        double r132278 = pow(r132267, r132262);
        double r132279 = r132251 / r132278;
        double r132280 = r132277 + r132279;
        double r132281 = 1.453152027;
        double r132282 = pow(r132267, r132241);
        double r132283 = r132281 / r132282;
        double r132284 = r132243 - r132283;
        double r132285 = r132280 + r132284;
        double r132286 = 0.284496736;
        double r132287 = r132286 / r132267;
        double r132288 = r132285 - r132287;
        double r132289 = pow(r132288, r132241);
        double r132290 = r132274 / r132289;
        double r132291 = r132240 / r132290;
        double r132292 = r132291 + r132242;
        double r132293 = r132266 * r132292;
        double r132294 = cbrt(r132268);
        double r132295 = 6.0;
        double r132296 = pow(r132294, r132295);
        double r132297 = r132266 / r132248;
        double r132298 = r132240 - r132297;
        double r132299 = r132240 * r132298;
        double r132300 = r132296 + r132299;
        double r132301 = r132300 * r132267;
        double r132302 = r132293 / r132301;
        double r132303 = r132240 * r132240;
        double r132304 = r132302 + r132303;
        double r132305 = r132272 / r132304;
        return r132305;
}

Error

Bits error versus x

Derivation

1. Initial program 13.9

   \[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

2. Simplified 13.9

   \[\leadsto \color{blue}{1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\]
3. Using strategy rm

4. Applied flip3-- 13.9

   \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{3}}{1 \cdot 1 + \left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1 \cdot \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}}\]

5. Simplified 13.9

   \[\leadsto \frac{\color{blue}{{1}^{3} - {\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{1 \cdot 1 + \left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1 \cdot \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}\]

6. Simplified 13.9

   \[\leadsto \frac{{1}^{3} - {\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}{\color{blue}{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} + 1\right) + 1 \cdot 1}}\]
7. Using strategy rm

8. Applied add-sqr-sqrt 13.1

   \[\leadsto \frac{{1}^{3} - \color{blue}{\sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}}{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} + 1\right) + 1 \cdot 1}\]
9. Using strategy rm

10. Applied flip3-+ 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \color{blue}{\frac{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3} + {1}^{3}}{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} + \left(1 \cdot 1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot 1\right)}} + 1 \cdot 1}\]

11. Applied frac-times 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\color{blue}{\frac{\left(1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left({\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3} + {1}^{3}\right)}{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right) \cdot \left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} + \left(1 \cdot 1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot 1\right)\right)}} + 1 \cdot 1}\]

12. Simplified 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\frac{\left(1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left({\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3} + {1}^{3}\right)}{\color{blue}{\left({\left(\sqrt[3]{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}}\right)}^{6} + 1 \cdot \left(1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}} + 1 \cdot 1}\]

13. Taylor expanded around 0 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\frac{\left(1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\color{blue}{1 \cdot \frac{{\left(\left(1.061405428999999900341322245367337018251 \cdot \frac{1}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}} + \left(1.421413741000000063863240029604639858007 \cdot \frac{1}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}} + 0.2548295919999999936678136691625695675611\right)\right) - \left(1.453152027000000012790792425221297889948 \cdot \frac{1}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + 0.2844967359999999723108032867457950487733 \cdot \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right)}^{3}}{{\left(e^{{\left(\left|x\right|\right)}^{2}}\right)}^{3} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}}} + {1}^{3}\right)}{\left({\left(\sqrt[3]{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}}\right)}^{6} + 1 \cdot \left(1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)} + 1 \cdot 1}\]

14. Simplified 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\frac{\left(1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\color{blue}{\frac{1}{\frac{{\left(e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)\right)}^{3}}{{\left(\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}} + \frac{1.421413741000000063863240029604639858007}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right) + \left(0.2548295919999999936678136691625695675611 - \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}}\right)\right) - \frac{0.2844967359999999723108032867457950487733}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}} + {1}^{3}\right)}{\left({\left(\sqrt[3]{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}}\right)}^{6} + 1 \cdot \left(1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)} + 1 \cdot 1}\]

15. Final simplification 13.1

    \[\leadsto \frac{{1}^{3} - \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}} \cdot \sqrt{{\left(\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}}{\frac{\left(1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}\right) \cdot \left(\frac{1}{\frac{{\left(e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)\right)}^{3}}{{\left(\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}} + \frac{1.421413741000000063863240029604639858007}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right) + \left(0.2548295919999999936678136691625695675611 - \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}}\right)\right) - \frac{0.2844967359999999723108032867457950487733}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)}^{3}}} + {1}^{3}\right)}{\left({\left(\sqrt[3]{\frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}}\right)}^{6} + 1 \cdot \left(1 - \frac{1 \cdot \frac{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)} + 1 \cdot 1}\]

Reproduce

herbie shell --seed 2019315 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 0.25482959199999999 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -0.284496735999999972 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 1.42141374100000006 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -1.45315202700000001 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) 1.0614054289999999))))))))) (exp (- (* (fabs x) (fabs x)))))))