Jmat.Real.erf

Average Error: 13.9 → 0.8

Time: 25.9s

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

C

double f(double x) {
        double r136349 = 1.0;
        double r136350 = 0.3275911;
        double r136351 = x;
        double r136352 = fabs(r136351);
        double r136353 = r136350 * r136352;
        double r136354 = r136349 + r136353;
        double r136355 = r136349 / r136354;
        double r136356 = 0.254829592;
        double r136357 = -0.284496736;
        double r136358 = 1.421413741;
        double r136359 = -1.453152027;
        double r136360 = 1.061405429;
        double r136361 = r136355 * r136360;
        double r136362 = r136359 + r136361;
        double r136363 = r136355 * r136362;
        double r136364 = r136358 + r136363;
        double r136365 = r136355 * r136364;
        double r136366 = r136357 + r136365;
        double r136367 = r136355 * r136366;
        double r136368 = r136356 + r136367;
        double r136369 = r136355 * r136368;
        double r136370 = r136352 * r136352;
        double r136371 = -r136370;
        double r136372 = exp(r136371);
        double r136373 = r136369 * r136372;
        double r136374 = r136349 - r136373;
        return r136374;
}

↓

double f(double x) {
        double r136375 = 1.0;
        double r136376 = 0.3275911;
        double r136377 = x;
        double r136378 = fabs(r136377);
        double r136379 = fma(r136376, r136378, r136375);
        double r136380 = r136375 / r136379;
        double r136381 = 1.061405429;
        double r136382 = -1.453152027;
        double r136383 = fma(r136381, r136380, r136382);
        double r136384 = r136380 * r136383;
        double r136385 = 1.421413741;
        double r136386 = r136384 + r136385;
        double r136387 = -0.284496736;
        double r136388 = fma(r136380, r136386, r136387);
        double r136389 = 0.254829592;
        double r136390 = fma(r136380, r136388, r136389);
        double r136391 = r136375 * r136390;
        double r136392 = -r136391;
        double r136393 = r136392 / r136379;
        double r136394 = exp(r136378);
        double r136395 = -2.0;
        double r136396 = r136395 * r136378;
        double r136397 = pow(r136394, r136396);
        double r136398 = r136379 / r136390;
        double r136399 = r136375 / r136398;
        double r136400 = r136397 * r136399;
        double r136401 = r136375 * r136375;
        double r136402 = fma(r136393, r136400, r136401);
        double r136403 = 2.0;
        double r136404 = pow(r136378, r136403);
        double r136405 = exp(r136404);
        double r136406 = r136380 / r136405;
        double r136407 = fma(r136406, r136390, r136375);
        double r136408 = r136402 / r136407;
        return r136408;
}

Error

Bits error versus x

Derivation

1. Initial program 13.9

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

3. Applied add-cube-cbrt 13.9

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

4. Simplified 13.9

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

5. Simplified 13.9

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

7. Applied flip-- 13.9

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

8. Simplified 0.8

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

9. Simplified 0.8

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

10. Final simplification 0.8

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))