Average Error: 13.9 → 13.0
Time: 1.2min
Precision: binary64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\frac{1 - {\left(\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}\right)}^{3}}{1 + \left(\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} + {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left(\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}\right)\right)}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}\]
1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{\frac{1 - {\left(\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}\right)}^{3}}{1 + \left(\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} + {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left(\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}\right)\right)}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}
(FPCore (x)
 :precision binary64
 (-
  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)))))))
↓
(FPCore (x)
 :precision binary64
 (/
  (/
   (-
    1.0
    (pow
     (*
      (sqrt
       (pow
        (/
         (/
          (+
           0.254829592
           (/
            (+
             -0.284496736
             (/
              (+
               1.421413741
               (/
                (+ -1.453152027 (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
                (+ 1.0 (* 0.3275911 (fabs x)))))
              (+ 1.0 (* 0.3275911 (fabs x)))))
            (+ 1.0 (* 0.3275911 (fabs x)))))
          (+ 1.0 (* 0.3275911 (fabs x))))
         (exp (pow (fabs x) 2.0)))
        3.0))
      (sqrt
       (*
        (/ 1.0 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2.0))
        (pow
         (/
          (/
           (+
            0.254829592
            (/
             (+
              -0.284496736
              (/
               (+
                1.421413741
                (/
                 (+
                  -1.453152027
                  (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
                 (+ 1.0 (* 0.3275911 (fabs x)))))
               (+ 1.0 (* 0.3275911 (fabs x)))))
             (+ 1.0 (* 0.3275911 (fabs x)))))
           (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
          (exp (pow (fabs x) 2.0)))
         3.0))))
     3.0))
   (+
    1.0
    (+
     (*
      (sqrt
       (pow
        (/
         (/
          (+
           0.254829592
           (/
            (+
             -0.284496736
             (/
              (+
               1.421413741
               (/
                (+ -1.453152027 (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
                (+ 1.0 (* 0.3275911 (fabs x)))))
              (+ 1.0 (* 0.3275911 (fabs x)))))
            (+ 1.0 (* 0.3275911 (fabs x)))))
          (+ 1.0 (* 0.3275911 (fabs x))))
         (exp (pow (fabs x) 2.0)))
        3.0))
      (sqrt
       (*
        (/ 1.0 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2.0))
        (pow
         (/
          (/
           (+
            0.254829592
            (/
             (+
              -0.284496736
              (/
               (+
                1.421413741
                (/
                 (+
                  -1.453152027
                  (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
                 (+ 1.0 (* 0.3275911 (fabs x)))))
               (+ 1.0 (* 0.3275911 (fabs x)))))
             (+ 1.0 (* 0.3275911 (fabs x)))))
           (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
          (exp (pow (fabs x) 2.0)))
         3.0))))
     (*
      (pow
       (/
        (/
         (+
          0.254829592
          (/
           (+
            -0.284496736
            (/
             (+
              1.421413741
              (/
               (+ -1.453152027 (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
               (+ 1.0 (* 0.3275911 (fabs x)))))
             (+ 1.0 (* 0.3275911 (fabs x)))))
           (+ 1.0 (* 0.3275911 (fabs x)))))
         (+ 1.0 (* 0.3275911 (fabs x))))
        (exp (pow (fabs x) 2.0)))
       3.0)
      (*
       (/ 1.0 (pow (+ 1.0 (* 0.3275911 (fabs x))) 2.0))
       (pow
        (/
         (/
          (+
           0.254829592
           (/
            (+
             -0.284496736
             (/
              (+
               1.421413741
               (/
                (+ -1.453152027 (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
                (+ 1.0 (* 0.3275911 (fabs x)))))
              (+ 1.0 (* 0.3275911 (fabs x)))))
            (+ 1.0 (* 0.3275911 (fabs x)))))
          (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
         (exp (pow (fabs x) 2.0)))
        3.0))))))
  (+
   1.0
   (*
    (/
     (/
      (+
       0.254829592
       (/
        (+
         -0.284496736
         (/
          (+
           1.421413741
           (/
            (+ -1.453152027 (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
            (+ 1.0 (* 0.3275911 (fabs x)))))
          (+ 1.0 (* 0.3275911 (fabs x)))))
        (+ 1.0 (* 0.3275911 (fabs x)))))
      (+ 1.0 (* 0.3275911 (fabs x))))
     (exp (pow (fabs x) 2.0)))
    (+
     1.0
     (/
      (/
       (+
        0.254829592
        (/
         (+
          -0.284496736
          (/
           (+
            1.421413741
            (/
             (+ -1.453152027 (/ 1.061405429 (+ 1.0 (* 0.3275911 (fabs x)))))
             (+ 1.0 (* 0.3275911 (fabs x)))))
           (+ 1.0 (* 0.3275911 (fabs x)))))
         (+ 1.0 (* 0.3275911 (fabs x)))))
       (+ 1.0 (* 0.3275911 (fabs x))))
      (exp (pow (fabs x) 2.0))))))))
double code(double x) {
	return 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))));
}
↓
double code(double x) {
	return ((1.0 - pow((sqrt(pow((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))), 3.0)) * sqrt((1.0 / pow((1.0 + (0.3275911 * fabs(x))), 2.0)) * pow((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))), 3.0))), 3.0)) / (1.0 + ((sqrt(pow((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))), 3.0)) * sqrt((1.0 / pow((1.0 + (0.3275911 * fabs(x))), 2.0)) * pow((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))), 3.0))) + (pow((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))), 3.0) * ((1.0 / pow((1.0 + (0.3275911 * fabs(x))), 2.0)) * pow((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))), 3.0)))))) / (1.0 + ((((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))) * (1.0 + (((0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / exp(pow(fabs(x), 2.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.9

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

  3. Applied flip3--_binary6413.9

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

  4. Simplified13.9

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

  5. Simplified13.9

    \[\leadsto \frac{1 - {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}{\color{blue}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt_binary6413.1

    \[\leadsto \frac{1 - \color{blue}{\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity_binary6413.1

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

  10. Applied add-cube-cbrt_binary6413.1

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

  11. Applied *-un-lft-identity_binary6413.1

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

  12. Applied times-frac_binary6413.1

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

  13. Applied times-frac_binary6413.1

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

  14. Applied unpow-prod-down_binary6413.1

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

  15. Simplified13.1

    \[\leadsto \frac{1 - \sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\color{blue}{{\left(\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}\right)}^{3}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}\]
  16. Using strategy rm

  17. Applied flip3--_binary6413.0

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

  18. Simplified13.0

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

  19. Simplified13.0

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

  20. Final simplification13.0

    \[\leadsto \frac{\frac{1 - {\left(\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}\right)}^{3}}{1 + \left(\sqrt{{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} + {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left(\frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}\right)\right)}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}\]

Reproduce

herbie shell --seed 2020231 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 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)))))))