Average Error: 13.6 → 12.7
Time: 2.2m
Precision: 64
\[1.0 - \left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\frac{{\left({\left(\sqrt{1.0}\right)}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{{\left(\sqrt{1.0}\right)}^{3} \cdot {\left(\sqrt{1.0}\right)}^{3} + \left({\left(\sqrt{1.0}\right)}^{3} \cdot \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} + \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}}\right)} \cdot \left(\sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} + {\left(\sqrt{1.0}\right)}^{3}\right)}{1.0 \cdot 1.0 + \left(\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)\right)}\]
1.0 - \left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{\frac{{\left({\left(\sqrt{1.0}\right)}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{{\left(\sqrt{1.0}\right)}^{3} \cdot {\left(\sqrt{1.0}\right)}^{3} + \left({\left(\sqrt{1.0}\right)}^{3} \cdot \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} + \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}}\right)} \cdot \left(\sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} + {\left(\sqrt{1.0}\right)}^{3}\right)}{1.0 \cdot 1.0 + \left(\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)\right)}
double f(double x) {
        double r7980371 = 1.0;
        double r7980372 = 0.3275911;
        double r7980373 = x;
        double r7980374 = fabs(r7980373);
        double r7980375 = r7980372 * r7980374;
        double r7980376 = r7980371 + r7980375;
        double r7980377 = r7980371 / r7980376;
        double r7980378 = 0.254829592;
        double r7980379 = -0.284496736;
        double r7980380 = 1.421413741;
        double r7980381 = -1.453152027;
        double r7980382 = 1.061405429;
        double r7980383 = r7980377 * r7980382;
        double r7980384 = r7980381 + r7980383;
        double r7980385 = r7980377 * r7980384;
        double r7980386 = r7980380 + r7980385;
        double r7980387 = r7980377 * r7980386;
        double r7980388 = r7980379 + r7980387;
        double r7980389 = r7980377 * r7980388;
        double r7980390 = r7980378 + r7980389;
        double r7980391 = r7980377 * r7980390;
        double r7980392 = r7980374 * r7980374;
        double r7980393 = -r7980392;
        double r7980394 = exp(r7980393);
        double r7980395 = r7980391 * r7980394;
        double r7980396 = r7980371 - r7980395;
        return r7980396;
}
↓
double f(double x) {
        double r7980397 = 1.0;
        double r7980398 = sqrt(r7980397);
        double r7980399 = 3.0;
        double r7980400 = pow(r7980398, r7980399);
        double r7980401 = pow(r7980400, r7980399);
        double r7980402 = x;
        double r7980403 = fabs(r7980402);
        double r7980404 = 0.3275911;
        double r7980405 = r7980403 * r7980404;
        double r7980406 = r7980397 + r7980405;
        double r7980407 = r7980397 / r7980406;
        double r7980408 = -0.284496736;
        double r7980409 = r7980397 - r7980405;
        double r7980410 = r7980397 * r7980397;
        double r7980411 = r7980405 * r7980405;
        double r7980412 = r7980410 - r7980411;
        double r7980413 = r7980397 / r7980412;
        double r7980414 = r7980409 * r7980413;
        double r7980415 = 1.061405429;
        double r7980416 = r7980414 * r7980415;
        double r7980417 = -1.453152027;
        double r7980418 = r7980416 + r7980417;
        double r7980419 = r7980418 * r7980407;
        double r7980420 = 1.421413741;
        double r7980421 = r7980419 + r7980420;
        double r7980422 = r7980407 * r7980421;
        double r7980423 = r7980408 + r7980422;
        double r7980424 = r7980407 * r7980423;
        double r7980425 = 0.254829592;
        double r7980426 = r7980424 + r7980425;
        double r7980427 = r7980426 * r7980407;
        double r7980428 = -r7980403;
        double r7980429 = r7980428 * r7980403;
        double r7980430 = exp(r7980429);
        double r7980431 = r7980427 * r7980430;
        double r7980432 = pow(r7980431, r7980399);
        double r7980433 = sqrt(r7980432);
        double r7980434 = pow(r7980433, r7980399);
        double r7980435 = r7980401 - r7980434;
        double r7980436 = r7980400 * r7980400;
        double r7980437 = r7980400 * r7980433;
        double r7980438 = r7980433 * r7980433;
        double r7980439 = r7980437 + r7980438;
        double r7980440 = r7980436 + r7980439;
        double r7980441 = r7980435 / r7980440;
        double r7980442 = r7980433 + r7980400;
        double r7980443 = r7980441 * r7980442;
        double r7980444 = r7980431 * r7980431;
        double r7980445 = r7980397 * r7980431;
        double r7980446 = r7980444 + r7980445;
        double r7980447 = r7980410 + r7980446;
        double r7980448 = r7980443 / r7980447;
        return r7980448;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.6

    \[1.0 - \left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied flip-+13.5

    \[\leadsto 1.0 - \left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1.0}{\color{blue}{\frac{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)}{1.0 - 0.3275911 \cdot \left|x\right|}}} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  4. Applied associate-/r/13.5

    \[\leadsto 1.0 - \left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{blue}{\left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right)} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  5. Using strategy rm

  6. Applied flip3--13.5

    \[\leadsto \color{blue}{\frac{{1.0}^{3} - {\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{1.0 \cdot 1.0 + \left(\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt12.8

    \[\leadsto \frac{{1.0}^{3} - \color{blue}{\sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}}{1.0 \cdot 1.0 + \left(\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\]

  9. Applied add-sqr-sqrt12.8

    \[\leadsto \frac{{\color{blue}{\left(\sqrt{1.0} \cdot \sqrt{1.0}\right)}}^{3} - \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}{1.0 \cdot 1.0 + \left(\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\]

  10. Applied unpow-prod-down12.8

    \[\leadsto \frac{\color{blue}{{\left(\sqrt{1.0}\right)}^{3} \cdot {\left(\sqrt{1.0}\right)}^{3}} - \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}{1.0 \cdot 1.0 + \left(\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\]

  11. Applied difference-of-squares12.8

    \[\leadsto \frac{\color{blue}{\left({\left(\sqrt{1.0}\right)}^{3} + \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right) \cdot \left({\left(\sqrt{1.0}\right)}^{3} - \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}}{1.0 \cdot 1.0 + \left(\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\]
  12. Using strategy rm

  13. Applied flip3--12.7

    \[\leadsto \frac{\left({\left(\sqrt{1.0}\right)}^{3} + \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right) \cdot \color{blue}{\frac{{\left({\left(\sqrt{1.0}\right)}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{{\left(\sqrt{1.0}\right)}^{3} \cdot {\left(\sqrt{1.0}\right)}^{3} + \left(\sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} + {\left(\sqrt{1.0}\right)}^{3} \cdot \sqrt{{\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}}}{1.0 \cdot 1.0 + \left(\left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1.0}{1.0 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\frac{1.0}{1.0 \cdot 1.0 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1.0 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\]

  14. Final simplification12.7

    \[\leadsto \frac{\frac{{\left({\left(\sqrt{1.0}\right)}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}}\right)}^{3}}{{\left(\sqrt{1.0}\right)}^{3} \cdot {\left(\sqrt{1.0}\right)}^{3} + \left({\left(\sqrt{1.0}\right)}^{3} \cdot \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} + \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}}\right)} \cdot \left(\sqrt{{\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)}^{3}} + {\left(\sqrt{1.0}\right)}^{3}\right)}{1.0 \cdot 1.0 + \left(\left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right) + 1.0 \cdot \left(\left(\left(\frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(-0.284496736 + \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(\left(\left(1.0 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1.0}{1.0 \cdot 1.0 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}\right) \cdot 1.061405429 + -1.453152027\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911} + 1.421413741\right)\right) + 0.254829592\right) \cdot \frac{1.0}{1.0 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|}\right)\right)}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))