Jmat.Real.erf

Average Error: 13.8 → 13.0

Time: 8.1m

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

C

double f(double x) {
        double r2613380 = 1.0;
        double r2613381 = 0.3275911;
        double r2613382 = x;
        double r2613383 = fabs(r2613382);
        double r2613384 = r2613381 * r2613383;
        double r2613385 = r2613380 + r2613384;
        double r2613386 = r2613380 / r2613385;
        double r2613387 = 0.254829592;
        double r2613388 = -0.284496736;
        double r2613389 = 1.421413741;
        double r2613390 = -1.453152027;
        double r2613391 = 1.061405429;
        double r2613392 = r2613386 * r2613391;
        double r2613393 = r2613390 + r2613392;
        double r2613394 = r2613386 * r2613393;
        double r2613395 = r2613389 + r2613394;
        double r2613396 = r2613386 * r2613395;
        double r2613397 = r2613388 + r2613396;
        double r2613398 = r2613386 * r2613397;
        double r2613399 = r2613387 + r2613398;
        double r2613400 = r2613386 * r2613399;
        double r2613401 = r2613383 * r2613383;
        double r2613402 = -r2613401;
        double r2613403 = exp(r2613402);
        double r2613404 = r2613400 * r2613403;
        double r2613405 = r2613380 - r2613404;
        return r2613405;
}

↓

double f(double x) {
        double r2613406 = 1.421413741;
        double r2613407 = 0.3275911;
        double r2613408 = x;
        double r2613409 = fabs(r2613408);
        double r2613410 = 1.0;
        double r2613411 = fma(r2613407, r2613409, r2613410);
        double r2613412 = 2.0;
        double r2613413 = pow(r2613411, r2613412);
        double r2613414 = r2613406 / r2613413;
        double r2613415 = 1.453152027;
        double r2613416 = 3.0;
        double r2613417 = pow(r2613411, r2613416);
        double r2613418 = r2613415 / r2613417;
        double r2613419 = 0.284496736;
        double r2613420 = r2613419 / r2613411;
        double r2613421 = r2613418 + r2613420;
        double r2613422 = 1.061405429;
        double r2613423 = 4.0;
        double r2613424 = pow(r2613411, r2613423);
        double r2613425 = r2613422 / r2613424;
        double r2613426 = r2613421 - r2613425;
        double r2613427 = r2613414 - r2613426;
        double r2613428 = 0.254829592;
        double r2613429 = r2613415 / r2613413;
        double r2613430 = -1.0;
        double r2613431 = r2613430 / r2613411;
        double r2613432 = fma(r2613429, r2613431, r2613418);
        double r2613433 = r2613428 + r2613432;
        double r2613434 = r2613427 + r2613433;
        double r2613435 = pow(r2613409, r2613412);
        double r2613436 = -r2613435;
        double r2613437 = exp(r2613436);
        double r2613438 = r2613410 / r2613411;
        double r2613439 = r2613437 * r2613438;
        double r2613440 = r2613434 * r2613439;
        double r2613441 = pow(r2613440, r2613416);
        double r2613442 = sqrt(r2613441);
        double r2613443 = 1.5;
        double r2613444 = pow(r2613410, r2613443);
        double r2613445 = r2613442 + r2613444;
        double r2613446 = r2613444 - r2613442;
        double r2613447 = r2613445 * r2613446;
        double r2613448 = fma(r2613409, r2613407, r2613410);
        double r2613449 = pow(r2613448, r2613423);
        double r2613450 = r2613422 / r2613449;
        double r2613451 = pow(r2613448, r2613412);
        double r2613452 = r2613406 / r2613451;
        double r2613453 = r2613419 / r2613448;
        double r2613454 = pow(r2613448, r2613416);
        double r2613455 = r2613415 / r2613454;
        double r2613456 = r2613453 + r2613455;
        double r2613457 = r2613452 - r2613456;
        double r2613458 = r2613457 + r2613428;
        double r2613459 = r2613450 + r2613458;
        double r2613460 = r2613430 / r2613448;
        double r2613461 = r2613415 / r2613451;
        double r2613462 = fma(r2613460, r2613461, r2613455);
        double r2613463 = r2613459 + r2613462;
        double r2613464 = r2613410 / r2613448;
        double r2613465 = r2613437 * r2613464;
        double r2613466 = fma(r2613463, r2613465, r2613410);
        double r2613467 = r2613463 * r2613437;
        double r2613468 = r2613467 * r2613464;
        double r2613469 = r2613466 * r2613468;
        double r2613470 = fma(r2613410, r2613410, r2613469);
        double r2613471 = r2613447 / r2613470;
        return r2613471;
}

Error

Bits error versus x

Derivation

1. Initial program 13.8

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

2. Taylor expanded around 0 14.5

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

3. Simplified 13.8

   \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \color{blue}{\left(\frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}} + \left(\left(\left(0.2548295919999999936678136691625695675611 + \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}\right) - \frac{0.2844967359999999723108032867457950487733}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right) - \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
4. Using strategy rm

5. Applied cube-mult 13.8

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

6. Applied *-un-lft-identity 13.8

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

7. Applied times-frac 13.8

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

8. Applied add-sqr-sqrt 14.5

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

9. Applied prod-diff 14.5

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

10. Simplified 13.8

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

11. Simplified 13.8

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}} + \left(\left(\left(\left(0.2548295919999999936678136691625695675611 + \frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}\right) - \frac{0.2844967359999999723108032867457950487733}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right) + \frac{-\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right) + \color{blue}{\mathsf{fma}\left(\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, \frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
12. Using strategy rm

13. Applied flip3-- 13.8

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

14. Simplified 13.8

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

15. Simplified 13.8

    \[\leadsto \frac{{1}^{3} - {\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} \cdot \left(\left(\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right) + \left(\left(0.2548295919999999936678136691625695675611 + \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} - \left(\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \frac{0.2844967359999999723108032867457950487733}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)\right)\right) + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)}^{3}}{\color{blue}{\mathsf{fma}\left(1, 1, \left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} \cdot \left(\left(\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right) + \left(\left(0.2548295919999999936678136691625695675611 + \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} - \left(\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \frac{0.2844967359999999723108032867457950487733}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)\right)\right) + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}}, \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right) + \left(\left(0.2548295919999999936678136691625695675611 + \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} - \left(\frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \frac{0.2844967359999999723108032867457950487733}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)}\right)\right)\right) + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}\right), \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} \cdot e^{-{\left(\left|x\right|\right)}^{2}}, 1\right)\right)}}\]
16. Using strategy rm

17. Applied add-sqr-sqrt 13.0

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

18. Applied sqr-pow 13.0

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

19. Applied difference-of-squares 13.0

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

20. Simplified 13.0

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

21. Simplified 13.0

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

22. Final simplification 13.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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)))))))