Average Error: 13.6 → 12.7
Time: 19.8s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]
1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}
double f(double x) {
        double r290416 = 1.0;
        double r290417 = 0.3275911;
        double r290418 = x;
        double r290419 = fabs(r290418);
        double r290420 = r290417 * r290419;
        double r290421 = r290416 + r290420;
        double r290422 = r290416 / r290421;
        double r290423 = 0.254829592;
        double r290424 = -0.284496736;
        double r290425 = 1.421413741;
        double r290426 = -1.453152027;
        double r290427 = 1.061405429;
        double r290428 = r290422 * r290427;
        double r290429 = r290426 + r290428;
        double r290430 = r290422 * r290429;
        double r290431 = r290425 + r290430;
        double r290432 = r290422 * r290431;
        double r290433 = r290424 + r290432;
        double r290434 = r290422 * r290433;
        double r290435 = r290423 + r290434;
        double r290436 = r290422 * r290435;
        double r290437 = r290419 * r290419;
        double r290438 = -r290437;
        double r290439 = exp(r290438);
        double r290440 = r290436 * r290439;
        double r290441 = r290416 - r290440;
        return r290441;
}
↓
double f(double x) {
        double r290442 = 1.0;
        double r290443 = 3.0;
        double r290444 = pow(r290442, r290443);
        double r290445 = pow(r290444, r290443);
        double r290446 = r290442 * r290442;
        double r290447 = 0.3275911;
        double r290448 = x;
        double r290449 = fabs(r290448);
        double r290450 = r290447 * r290449;
        double r290451 = r290450 * r290450;
        double r290452 = r290446 - r290451;
        double r290453 = r290442 / r290452;
        double r290454 = r290442 - r290450;
        double r290455 = fma(r290447, r290449, r290442);
        double r290456 = 2.0;
        double r290457 = pow(r290455, r290456);
        double r290458 = r290457 / r290442;
        double r290459 = r290442 / r290458;
        double r290460 = r290442 / r290455;
        double r290461 = 1.061405429;
        double r290462 = -1.453152027;
        double r290463 = fma(r290460, r290461, r290462);
        double r290464 = 1.421413741;
        double r290465 = fma(r290460, r290463, r290464);
        double r290466 = -0.284496736;
        double r290467 = r290466 * r290442;
        double r290468 = r290467 / r290455;
        double r290469 = fma(r290459, r290465, r290468);
        double r290470 = 0.254829592;
        double r290471 = r290470 * r290454;
        double r290472 = fma(r290454, r290469, r290471);
        double r290473 = r290453 * r290472;
        double r290474 = r290449 * r290449;
        double r290475 = -r290474;
        double r290476 = exp(r290475);
        double r290477 = r290473 * r290476;
        double r290478 = pow(r290477, r290443);
        double r290479 = sqrt(r290478);
        double r290480 = r290479 * r290479;
        double r290481 = pow(r290480, r290443);
        double r290482 = r290445 - r290481;
        double r290483 = r290478 + r290444;
        double r290484 = 6.0;
        double r290485 = pow(r290442, r290484);
        double r290486 = fma(r290478, r290483, r290485);
        double r290487 = r290482 / r290486;
        double r290488 = r290469 + r290470;
        double r290489 = r290454 * r290488;
        double r290490 = r290489 * r290442;
        double r290491 = r290455 * r290454;
        double r290492 = r290490 / r290491;
        double r290493 = pow(r290449, r290456);
        double r290494 = exp(r290493);
        double r290495 = r290492 / r290494;
        double r290496 = r290442 / r290491;
        double r290497 = 1.0;
        double r290498 = r290489 * r290497;
        double r290499 = r290498 / r290494;
        double r290500 = fma(r290496, r290499, r290442);
        double r290501 = r290495 * r290500;
        double r290502 = r290501 + r290446;
        double r290503 = r290487 / r290502;
        return r290503;
}

Error

Bits error versus x

Derivation

  1. Initial program 13.6

    \[1 - \left(\frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied flip-+13.6

    \[\leadsto 1 - \left(\frac{1}{\color{blue}{\frac{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)}{1 - 0.32759110000000002 \cdot \left|x\right|}}} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  4. Applied associate-/r/13.6

    \[\leadsto 1 - \left(\color{blue}{\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)} \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  5. Applied associate-*l*13.6

    \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.25482959199999999 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-0.284496735999999972 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(1.42141374100000006 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot \left(-1.45315202700000001 + \frac{1}{1 + 0.32759110000000002 \cdot \left|x\right|} \cdot 1.0614054289999999\right)\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  6. Simplified13.6

    \[\leadsto 1 - \left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \color{blue}{\mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  7. Using strategy rm

  8. Applied flip3--13.6

    \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{1 \cdot 1 + \left(\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1 \cdot \left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}}\]

  9. Simplified13.6

    \[\leadsto \frac{{1}^{3} - {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{blue}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}}\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt12.8

    \[\leadsto \frac{{1}^{3} - \color{blue}{\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]
  12. Using strategy rm

  13. Applied flip3--12.7

    \[\leadsto \frac{\color{blue}{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{{1}^{3} \cdot {1}^{3} + \left(\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right) \cdot \left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right) + {1}^{3} \cdot \left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)\right)}}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]

  14. Simplified12.7

    \[\leadsto \frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\color{blue}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]

  15. Final simplification12.7

    \[\leadsto \frac{\frac{{\left({1}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{\mathsf{fma}\left({\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}, {\left(\left(\frac{1}{1 \cdot 1 - \left(0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(0.32759110000000002 \cdot \left|x\right|\right)} \cdot \mathsf{fma}\left(1 - 0.32759110000000002 \cdot \left|x\right|, \mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right), 0.25482959199999999 \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3} + {1}^{3}, {1}^{6}\right)}}{\frac{\frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right) \cdot \left(1 - 0.32759110000000002 \cdot \left|x\right|\right)}, \frac{\left(\left(1 - 0.32759110000000002 \cdot \left|x\right|\right) \cdot \left(\mathsf{fma}\left(\frac{1}{\frac{{\left(\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)\right)}^{2}}{1}}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, \mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}, 1.0614054289999999, -1.45315202700000001\right), 1.42141374100000006\right), \frac{-0.284496735999999972 \cdot 1}{\mathsf{fma}\left(0.32759110000000002, \left|x\right|, 1\right)}\right) + 0.25482959199999999\right)\right) \cdot 1}{e^{{\left(\left|x\right|\right)}^{2}}}, 1\right) + 1 \cdot 1}\]

Reproduce

herbie shell --seed 2020049 +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)))))))