Average Error: 13.8 → 11.7
Time: 18.4s
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(\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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left({\left(\frac{\sqrt{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|}\right)}^{3} \cdot {\left(\frac{\sqrt{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|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}\right)}{1 + \sqrt{{\left(\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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{{\left(\frac{\sqrt{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|}\right)}^{3} \cdot {\left(\frac{\sqrt{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|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}}{1 + \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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot 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(\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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3} \cdot \left({\left(\frac{\sqrt{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|}\right)}^{3} \cdot {\left(\frac{\sqrt{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|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}\right)}{1 + \sqrt{{\left(\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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{{\left(\frac{\sqrt{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|}\right)}^{3} \cdot {\left(\frac{\sqrt{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|}}}{e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}}{1 + \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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \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|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot 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
      (/
       (+
        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)
     (*
      (pow
       (/
        (sqrt
         (+
          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))))
       3.0)
      (pow
       (/
        (sqrt
         (+
          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))))))
        (exp (pow (fabs x) 2.0)))
       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
      (*
       (pow
        (/
         (sqrt
          (+
           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))))
        3.0)
       (pow
        (/
         (sqrt
          (+
           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))))))
         (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 ((double) (1.0 - ((double) (((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))))) * ((double) exp(((double) -(((double) (((double) fabs(x)) * ((double) fabs(x))))))))))));
}
↓
double code(double x) {
	return ((((double) (1.0 - ((double) (((double) pow((((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))) * ((double) exp(((double) pow(((double) fabs(x)), 2.0))))))), 3.0)) * ((double) (((double) pow((((double) sqrt(((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))), 3.0)) * ((double) pow((((double) sqrt(((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))))) / ((double) exp(((double) pow(((double) fabs(x)), 2.0))))), 3.0)))))))) / ((double) (1.0 + ((double) (((double) sqrt(((double) pow((((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))) * ((double) exp(((double) pow(((double) fabs(x)), 2.0))))))), 3.0)))) * ((double) sqrt(((double) (((double) pow((((double) sqrt(((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))), 3.0)) * ((double) pow((((double) sqrt(((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))))) / ((double) exp(((double) pow(((double) fabs(x)), 2.0))))), 3.0))))))))))) / ((double) (1.0 + ((double) ((((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))) * ((double) exp(((double) pow(((double) fabs(x)), 2.0))))))) * ((double) (1.0 + (((double) (0.254829592 + (((double) (-0.284496736 + (((double) (1.421413741 + (((double) (-1.453152027 + (1.061405429 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))))) / ((double) (((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))) * ((double) exp(((double) pow(((double) 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 13.8

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

  2. Simplified13.8

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

  4. Applied flip3--_binary6413.8

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

  5. Simplified13.8

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

  6. Simplified13.8

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

  8. Applied add-sqr-sqrt_binary6413.0

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

  10. Applied add-sqr-sqrt_binary6413.1

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

  11. Applied times-frac_binary6413.1

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

  12. Applied unpow-prod-down_binary6413.1

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

  14. Applied flip--_binary6413.1

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

  15. Simplified11.7

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

  16. Final simplification11.7

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

Reproduce

herbie shell --seed 2020210 
(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)))))))