Jmat.Real.erf

Average Error: 13.8 → 12.8

Time: 30.8s

Precision: 64

Math

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

↓

\[\left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} + \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}} \cdot \sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} - \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}}\right)\]

C

double f(double x) {
        double r209343 = 1.0;
        double r209344 = 0.3275911;
        double r209345 = x;
        double r209346 = fabs(r209345);
        double r209347 = r209344 * r209346;
        double r209348 = r209343 + r209347;
        double r209349 = r209343 / r209348;
        double r209350 = 0.254829592;
        double r209351 = -0.284496736;
        double r209352 = 1.421413741;
        double r209353 = -1.453152027;
        double r209354 = 1.061405429;
        double r209355 = r209349 * r209354;
        double r209356 = r209353 + r209355;
        double r209357 = r209349 * r209356;
        double r209358 = r209352 + r209357;
        double r209359 = r209349 * r209358;
        double r209360 = r209351 + r209359;
        double r209361 = r209349 * r209360;
        double r209362 = r209350 + r209361;
        double r209363 = r209349 * r209362;
        double r209364 = r209346 * r209346;
        double r209365 = -r209364;
        double r209366 = exp(r209365);
        double r209367 = r209363 * r209366;
        double r209368 = r209343 - r209367;
        return r209368;
}

↓

double f(double x) {
        double r209369 = x;
        double r209370 = fabs(r209369);
        double r209371 = 2.0;
        double r209372 = pow(r209370, r209371);
        double r209373 = -r209372;
        double r209374 = exp(r209373);
        double r209375 = 0.284496736;
        double r209376 = 0.3275911;
        double r209377 = 1.0;
        double r209378 = fma(r209370, r209376, r209377);
        double r209379 = pow(r209378, r209371);
        double r209380 = r209375 / r209379;
        double r209381 = 1.453152027;
        double r209382 = 4.0;
        double r209383 = pow(r209378, r209382);
        double r209384 = r209381 / r209383;
        double r209385 = r209380 + r209384;
        double r209386 = fma(r209374, r209385, r209377);
        double r209387 = 1.061405429;
        double r209388 = 5.0;
        double r209389 = pow(r209378, r209388);
        double r209390 = r209387 / r209389;
        double r209391 = 0.254829592;
        double r209392 = fma(r209376, r209370, r209377);
        double r209393 = r209391 / r209392;
        double r209394 = r209390 + r209393;
        double r209395 = 1.421413741;
        double r209396 = exp(r209372);
        double r209397 = 3.0;
        double r209398 = pow(r209378, r209397);
        double r209399 = r209396 * r209398;
        double r209400 = r209395 / r209399;
        double r209401 = fma(r209374, r209394, r209400);
        double r209402 = r209386 - r209401;
        double r209403 = cbrt(r209402);
        double r209404 = r209403 * r209403;
        double r209405 = sqrt(r209386);
        double r209406 = r209395 / r209398;
        double r209407 = r209391 / r209378;
        double r209408 = r209407 + r209390;
        double r209409 = r209406 + r209408;
        double r209410 = r209374 * r209409;
        double r209411 = sqrt(r209410);
        double r209412 = r209405 + r209411;
        double r209413 = cbrt(r209412);
        double r209414 = r209405 - r209411;
        double r209415 = cbrt(r209414);
        double r209416 = r209413 * r209415;
        double r209417 = r209404 * r209416;
        return r209417;
}

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. Simplified 13.8

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

3. Taylor expanded around 0 13.8

   \[\leadsto \color{blue}{\left(1 + \left(1.453152027000000012790792425221297889948 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{4}} + 0.2844967359999999723108032867457950487733 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(1.421413741000000063863240029604639858007 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \left(1.061405428999999900341322245367337018251 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{5}} + 0.2548295919999999936678136691625695675611 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}\right)\right)}\]

4. Simplified 13.8

   \[\leadsto \color{blue}{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{2}} + \frac{1.453152027000000012790792425221297889948}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\]
5. Using strategy rm

6. Applied add-cube-cbrt 13.8

   \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}}\]
7. Using strategy rm

8. Applied add-sqr-sqrt 13.8

   \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \color{blue}{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}}}\]

9. Applied add-sqr-sqrt 14.2

   \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \sqrt[3]{\color{blue}{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} \cdot \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)}} - \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}}\]

10. Applied difference-of-squares 12.8

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} + \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} - \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right)}}\]

11. Applied cbrt-prod 12.8

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} + \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}} \cdot \sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} - \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}}\right)}\]

12. Simplified 12.8

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\color{blue}{\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} + \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}}} \cdot \sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} - \sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}}\right)\]

13. Simplified 12.8

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} + \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}} \cdot \color{blue}{\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} - \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}}}\right)\]

14. Final simplification 12.8

    \[\leadsto \left(\sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right) - \mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}} + \frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(0.3275911000000000239396058532292954623699, \left|x\right|, 1\right)}, \frac{1.421413741000000063863240029604639858007}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}}\right)}\right) \cdot \left(\sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} + \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}} \cdot \sqrt[3]{\sqrt{\mathsf{fma}\left(e^{-{\left(\left|x\right|\right)}^{2}}, \frac{0.2844967359999999723108032867457950487733}{{\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)}^{4}}, 1\right)} - \sqrt{e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1.421413741000000063863240029604639858007}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{3}} + \left(\frac{0.2548295919999999936678136691625695675611}{\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)} + \frac{1.061405428999999900341322245367337018251}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911000000000239396058532292954623699, 1\right)\right)}^{5}}\right)\right)}}\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 0.25482959199999999 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -0.284496735999999972 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 1.42141374100000006 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -1.45315202700000001 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) 1.0614054289999999))))))))) (exp (- (* (fabs x) (fabs x)))))))