Jmat.Real.erf

Average Error: 13.7 → 9.8

Time: 2.4m

Precision: 64

Math

\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

↓

\[\sqrt[3]{\left(1 - \frac{\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}}\right) + \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \left(\frac{-\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)} \cdot \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\left(\left(\left(\frac{1.453152027}{\left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{e^{\left|x\right| \cdot \left|x\right|} \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}\right) + \frac{0.284496736}{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\right)\]

C

double f(double x) {
        double r5221524 = 1.0;
        double r5221525 = 0.3275911;
        double r5221526 = x;
        double r5221527 = fabs(r5221526);
        double r5221528 = r5221525 * r5221527;
        double r5221529 = r5221524 + r5221528;
        double r5221530 = r5221524 / r5221529;
        double r5221531 = 0.254829592;
        double r5221532 = -0.284496736;
        double r5221533 = 1.421413741;
        double r5221534 = -1.453152027;
        double r5221535 = 1.061405429;
        double r5221536 = r5221530 * r5221535;
        double r5221537 = r5221534 + r5221536;
        double r5221538 = r5221530 * r5221537;
        double r5221539 = r5221533 + r5221538;
        double r5221540 = r5221530 * r5221539;
        double r5221541 = r5221532 + r5221540;
        double r5221542 = r5221530 * r5221541;
        double r5221543 = r5221531 + r5221542;
        double r5221544 = r5221530 * r5221543;
        double r5221545 = r5221527 * r5221527;
        double r5221546 = -r5221545;
        double r5221547 = exp(r5221546);
        double r5221548 = r5221544 * r5221547;
        double r5221549 = r5221524 - r5221548;
        return r5221549;
}

↓

double f(double x) {
        double r5221550 = 1.0;
        double r5221551 = 0.3275911;
        double r5221552 = x;
        double r5221553 = fabs(r5221552);
        double r5221554 = fma(r5221551, r5221553, r5221550);
        double r5221555 = r5221550 / r5221554;
        double r5221556 = r5221553 * r5221553;
        double r5221557 = exp(r5221556);
        double r5221558 = 1.061405429;
        double r5221559 = r5221558 / r5221554;
        double r5221560 = -1.453152027;
        double r5221561 = r5221559 + r5221560;
        double r5221562 = 1.421413741;
        double r5221563 = fma(r5221561, r5221555, r5221562);
        double r5221564 = -0.284496736;
        double r5221565 = fma(r5221555, r5221563, r5221564);
        double r5221566 = 0.254829592;
        double r5221567 = fma(r5221565, r5221555, r5221566);
        double r5221568 = r5221557 / r5221567;
        double r5221569 = r5221555 / r5221568;
        double r5221570 = r5221550 - r5221569;
        double r5221571 = -r5221567;
        double r5221572 = r5221571 / r5221557;
        double r5221573 = r5221567 / r5221557;
        double r5221574 = r5221572 + r5221573;
        double r5221575 = r5221555 * r5221574;
        double r5221576 = r5221570 + r5221575;
        double r5221577 = cbrt(r5221576);
        double r5221578 = r5221573 / r5221554;
        double r5221579 = r5221550 - r5221578;
        double r5221580 = exp(r5221579);
        double r5221581 = log(r5221580);
        double r5221582 = cbrt(r5221581);
        double r5221583 = 1.453152027;
        double r5221584 = r5221554 * r5221554;
        double r5221585 = r5221584 * r5221584;
        double r5221586 = r5221585 * r5221557;
        double r5221587 = r5221583 / r5221586;
        double r5221588 = r5221587 + r5221550;
        double r5221589 = r5221553 * r5221551;
        double r5221590 = fma(r5221589, r5221557, r5221557);
        double r5221591 = r5221566 / r5221590;
        double r5221592 = 5.0;
        double r5221593 = pow(r5221554, r5221592);
        double r5221594 = r5221557 * r5221593;
        double r5221595 = r5221558 / r5221594;
        double r5221596 = r5221591 + r5221595;
        double r5221597 = r5221588 - r5221596;
        double r5221598 = r5221584 * r5221557;
        double r5221599 = r5221554 * r5221598;
        double r5221600 = r5221562 / r5221599;
        double r5221601 = r5221597 - r5221600;
        double r5221602 = 0.284496736;
        double r5221603 = r5221602 / r5221598;
        double r5221604 = r5221601 + r5221603;
        double r5221605 = cbrt(r5221604);
        double r5221606 = r5221582 * r5221605;
        double r5221607 = r5221577 * r5221606;
        return r5221607;
}

Error

Bits error versus x

Derivation

1. Initial program 13.7

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

2. Simplified 13.6

   \[\leadsto \color{blue}{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\]
3. Using strategy rm

4. Applied add-log-exp 13.6

   \[\leadsto \color{blue}{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)}\]
5. Using strategy rm

6. Applied add-cube-cbrt 13.6

   \[\leadsto \color{blue}{\left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)}\right) \cdot \sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)}}\]

7. Taylor expanded around 0 13.6

   \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\color{blue}{\left(1.453152027 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.421413741 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + \left(1.061405429 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + 0.254829592 \cdot \frac{1}{e^{{\left(\left|x\right|\right)}^{2}} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}\right)\right)}}\right) \cdot \sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)}\]

8. Simplified 10.2

   \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\color{blue}{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}}\right) \cdot \sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)}\]
9. Using strategy rm

10. Applied div-inv 10.2

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\log \left(e^{1 - \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}}\right)}\]

11. Applied add-cube-cbrt 10.2

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\log \left(e^{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}} - \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}} \cdot \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)}\]

12. Applied prod-diff 10.2

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\log \left(e^{\color{blue}{\mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right) + \mathsf{fma}\left(-\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}}\right)}\]

13. Applied exp-sum 10.2

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\log \color{blue}{\left(e^{\mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)} \cdot e^{\mathsf{fma}\left(-\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}\right)}}\]

14. Applied log-prod 10.2

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\color{blue}{\log \left(e^{\mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}\right) + \log \left(e^{\mathsf{fma}\left(-\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}\right)}}\]

15. Simplified 9.8

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(1 - \frac{\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}}\right)} + \log \left(e^{\mathsf{fma}\left(-\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}\right)}\]

16. Simplified 9.8

    \[\leadsto \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)} + \left(\left(\left(\frac{1.453152027}{e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5} \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(e^{\left|x\right| \cdot \left|x\right|} \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right)}\right)}\right) \cdot \sqrt[3]{\left(1 - \frac{\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}}\right) + \color{blue}{\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \left(\left(-\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right) + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)}}\]

17. Final simplification 9.8

    \[\leadsto \sqrt[3]{\left(1 - \frac{\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}}\right) + \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot \left(\frac{-\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}} + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}\right)} \cdot \left(\sqrt[3]{\log \left(e^{1 - \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027, \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1.421413741\right), -0.284496736\right), \frac{1}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}\right)} \cdot \sqrt[3]{\left(\left(\left(\frac{1.453152027}{\left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot \left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(\left|x\right| \cdot 0.3275911, e^{\left|x\right| \cdot \left|x\right|}, e^{\left|x\right| \cdot \left|x\right|}\right)} + \frac{1.061405429}{e^{\left|x\right| \cdot \left|x\right|} \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{5}}\right)\right) - \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \left(\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}\right)}\right) + \frac{0.284496736}{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}}\right)\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 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)))))))