Jmat.Real.erf

Average Error: 14.0 → 13.1

Time: 6.9m

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

C

double f(double x) {
        double r17439316 = 1.0;
        double r17439317 = 0.3275911;
        double r17439318 = x;
        double r17439319 = fabs(r17439318);
        double r17439320 = r17439317 * r17439319;
        double r17439321 = r17439316 + r17439320;
        double r17439322 = r17439316 / r17439321;
        double r17439323 = 0.254829592;
        double r17439324 = -0.284496736;
        double r17439325 = 1.421413741;
        double r17439326 = -1.453152027;
        double r17439327 = 1.061405429;
        double r17439328 = r17439322 * r17439327;
        double r17439329 = r17439326 + r17439328;
        double r17439330 = r17439322 * r17439329;
        double r17439331 = r17439325 + r17439330;
        double r17439332 = r17439322 * r17439331;
        double r17439333 = r17439324 + r17439332;
        double r17439334 = r17439322 * r17439333;
        double r17439335 = r17439323 + r17439334;
        double r17439336 = r17439322 * r17439335;
        double r17439337 = r17439319 * r17439319;
        double r17439338 = -r17439337;
        double r17439339 = exp(r17439338);
        double r17439340 = r17439336 * r17439339;
        double r17439341 = r17439316 - r17439340;
        return r17439341;
}

↓

double f(double x) {
        double r17439342 = 1.0;
        double r17439343 = 3.0;
        double r17439344 = pow(r17439342, r17439343);
        double r17439345 = pow(r17439344, r17439343);
        double r17439346 = pow(r17439345, r17439343);
        double r17439347 = x;
        double r17439348 = fabs(r17439347);
        double r17439349 = 0.3275911;
        double r17439350 = r17439348 * r17439349;
        double r17439351 = r17439342 + r17439350;
        double r17439352 = r17439342 / r17439351;
        double r17439353 = 0.254829592;
        double r17439354 = 1.061405429;
        double r17439355 = r17439352 * r17439354;
        double r17439356 = -1.453152027;
        double r17439357 = r17439355 + r17439356;
        double r17439358 = r17439352 * r17439357;
        double r17439359 = 1.421413741;
        double r17439360 = r17439358 + r17439359;
        double r17439361 = r17439352 * r17439360;
        double r17439362 = -0.284496736;
        double r17439363 = r17439361 + r17439362;
        double r17439364 = r17439352 * r17439363;
        double r17439365 = r17439353 + r17439364;
        double r17439366 = r17439352 * r17439365;
        double r17439367 = r17439348 * r17439348;
        double r17439368 = -r17439367;
        double r17439369 = exp(r17439368);
        double r17439370 = r17439366 * r17439369;
        double r17439371 = pow(r17439370, r17439343);
        double r17439372 = sqrt(r17439371);
        double r17439373 = r17439372 * r17439372;
        double r17439374 = pow(r17439373, r17439343);
        double r17439375 = pow(r17439374, r17439343);
        double r17439376 = r17439346 - r17439375;
        double r17439377 = r17439374 * r17439374;
        double r17439378 = r17439345 * r17439374;
        double r17439379 = r17439377 + r17439378;
        double r17439380 = r17439345 * r17439345;
        double r17439381 = r17439379 + r17439380;
        double r17439382 = r17439376 / r17439381;
        double r17439383 = r17439373 * r17439373;
        double r17439384 = r17439344 * r17439373;
        double r17439385 = r17439383 + r17439384;
        double r17439386 = r17439344 * r17439344;
        double r17439387 = r17439385 + r17439386;
        double r17439388 = r17439382 / r17439387;
        double r17439389 = r17439342 * r17439342;
        double r17439390 = r17439370 * r17439370;
        double r17439391 = r17439342 * r17439370;
        double r17439392 = r17439390 + r17439391;
        double r17439393 = r17439389 + r17439392;
        double r17439394 = r17439388 / r17439393;
        return r17439394;
}

Error

Bits error versus x

Derivation

1. Initial program 14.0

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

3. Applied flip3-- 14.0

   \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\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|}\right)}^{3}}{1 \cdot 1 + \left(\left(\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|}\right) \cdot \left(\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|}\right) + 1 \cdot \left(\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|}\right)\right)}}\]
4. Using strategy rm

5. Applied add-sqr-sqrt 13.2

   \[\leadsto \frac{{1}^{3} - \color{blue}{\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}}}{1 \cdot 1 + \left(\left(\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|}\right) \cdot \left(\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|}\right) + 1 \cdot \left(\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|}\right)\right)}\]
6. Using strategy rm

7. Applied flip3-- 13.1

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

9. Applied flip3-- 13.1

   \[\leadsto \frac{\frac{\color{blue}{\frac{{\left({\left({1}^{3}\right)}^{3}\right)}^{3} - {\left({\left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right)}^{3}\right)}^{3}}{{\left({1}^{3}\right)}^{3} \cdot {\left({1}^{3}\right)}^{3} + \left({\left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right)}^{3} \cdot {\left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right)}^{3} + {\left({1}^{3}\right)}^{3} \cdot {\left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right)}^{3}\right)}}}{{1}^{3} \cdot {1}^{3} + \left(\left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right) \cdot \left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\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|}\right)}^{3}} \cdot \sqrt{{\left(\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|}\right)}^{3}}\right)\right)}}{1 \cdot 1 + \left(\left(\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|}\right) \cdot \left(\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|}\right) + 1 \cdot \left(\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|}\right)\right)}\]

10. Final simplification 13.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))