Average Error: 13.8 → 13.8
Time: 32.0min
Precision: binary64
Cost: 245568
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\left(1 + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right) \cdot \left(1 - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]
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{\left(1 + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\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|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right) \cdot \left(1 - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\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|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\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|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\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|}}{{\left(e^{x}\right)}^{x}}\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
      (/
       (/
        (+
         (+ 0.254829592 (/ -0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))
         (/
          (/
           (+
            1.421413741
            (/
             (+
              -1.453152027
              (*
               1.061405429
               (/
                (- 1.0 (* 0.3275911 (fabs x)))
                (- 1.0 (* x (* x 0.10731592879921002))))))
             (+ 1.0 (* 0.3275911 (fabs x)))))
           (+ 1.0 (* 0.3275911 (fabs x))))
          (+ 1.0 (* 0.3275911 (fabs x)))))
        (+ 1.0 (* 0.3275911 (fabs x))))
       (pow (exp x) x)))
     3.0))
   (-
    1.0
    (pow
     (sqrt
      (/
       (/
        (+
         (+ 0.254829592 (/ -0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))
         (/
          (/
           (+
            1.421413741
            (/
             (+
              -1.453152027
              (*
               1.061405429
               (/
                (- 1.0 (* 0.3275911 (fabs x)))
                (- 1.0 (* x (* x 0.10731592879921002))))))
             (+ 1.0 (* 0.3275911 (fabs x)))))
           (+ 1.0 (* 0.3275911 (fabs x))))
          (+ 1.0 (* 0.3275911 (fabs x)))))
        (+ 1.0 (* 0.3275911 (fabs x))))
       (pow (exp x) x)))
     3.0)))
  (+
   1.0
   (*
    (/
     (/
      (+
       (+ 0.254829592 (/ -0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))
       (/
        (/
         (+
          1.421413741
          (/
           (+
            -1.453152027
            (*
             1.061405429
             (/
              (- 1.0 (* 0.3275911 (fabs x)))
              (- 1.0 (* x (* x 0.10731592879921002))))))
           (+ 1.0 (* 0.3275911 (fabs x)))))
         (+ 1.0 (* 0.3275911 (fabs x))))
        (+ 1.0 (* 0.3275911 (fabs x)))))
      (+ 1.0 (* 0.3275911 (fabs x))))
     (pow (exp x) x))
    (+
     1.0
     (/
      (/
       (+
        (+ 0.254829592 (/ -0.284496736 (+ 1.0 (* 0.3275911 (fabs x)))))
        (/
         (/
          (+
           1.421413741
           (/
            (+
             -1.453152027
             (*
              1.061405429
              (/
               (- 1.0 (* 0.3275911 (fabs x)))
               (- 1.0 (* x (* x 0.10731592879921002))))))
            (+ 1.0 (* 0.3275911 (fabs x)))))
          (+ 1.0 (* 0.3275911 (fabs x))))
         (+ 1.0 (* 0.3275911 (fabs x)))))
       (+ 1.0 (* 0.3275911 (fabs x))))
      (pow (exp x) x)))))))
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((((0.254829592 + (-0.284496736 / (1.0 + (0.3275911 * fabs(x))))) + (((1.421413741 + ((-1.453152027 + (1.061405429 * ((1.0 - (0.3275911 * fabs(x))) / (1.0 - (x * (x * 0.10731592879921002)))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / pow(exp(x), x)), 3.0)) * (1.0 - pow(sqrt((((0.254829592 + (-0.284496736 / (1.0 + (0.3275911 * fabs(x))))) + (((1.421413741 + ((-1.453152027 + (1.061405429 * ((1.0 - (0.3275911 * fabs(x))) / (1.0 - (x * (x * 0.10731592879921002)))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / pow(exp(x), x)), 3.0))) / (1.0 + (((((0.254829592 + (-0.284496736 / (1.0 + (0.3275911 * fabs(x))))) + (((1.421413741 + ((-1.453152027 + (1.061405429 * ((1.0 - (0.3275911 * fabs(x))) / (1.0 - (x * (x * 0.10731592879921002)))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / pow(exp(x), x)) * (1.0 + ((((0.254829592 + (-0.284496736 / (1.0 + (0.3275911 * fabs(x))))) + (((1.421413741 + ((-1.453152027 + (1.061405429 * ((1.0 - (0.3275911 * fabs(x))) / (1.0 - (x * (x * 0.10731592879921002)))))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x)))) / pow(exp(x), x)))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error13.8
Cost232768
\[\frac{\left(1 + {\left(\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}^{1.5}\right) \cdot \left(1 - {\left(\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}^{1.5}\right)}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]
Alternative 2
Error13.8
Cost49280
\[1 - e^{-x \cdot x} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + 1.061405429 \cdot \left(\left(1 - 0.3275911 \cdot \left|x\right|\right) \cdot \frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}\right)\right)\right)\right)\right)\right)\]
Alternative 3
Error13.8
Cost48768
\[1 - e^{-x \cdot x} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + 1.061405429 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)\right)\right)\right)\right)\]
Alternative 4
Error13.8
Cost47936
\[1 - e^{-x \cdot x} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \left(\frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|} + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)\right)\right)\]
Alternative 5
Error13.8
Cost41984
\[1 - e^{-x \cdot x} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + 1.061405429 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)\right)\right)\right)\right)\]
Alternative 6
Error13.8
Cost41280
\[1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{x \cdot x}}\]
Alternative 7
Error28.4
Cost64
\[1\]

Error

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. Using strategy rm

  3. Applied distribute-rgt-in_binary64_207413.8

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

  4. Applied associate-+r+_binary64_205613.8

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

  5. Simplified13.8

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

  7. Applied flip-+_binary64_209813.8

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

  8. Applied associate-/r/_binary64_207013.8

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

  9. Simplified13.8

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \left(\color{blue}{\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  10. Using strategy rm

  11. Applied flip3--_binary64_212813.8

    \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\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(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\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(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\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(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}}\]

  12. Simplified13.8

    \[\leadsto \frac{\color{blue}{1 - {\left(\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 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(e^{x}\right)}^{x}}\right)}^{3}}}{1 \cdot 1 + \left(\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\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(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\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(\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \left(\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 + \left(\frac{1}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right) \cdot 1.061405429\right)\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}\]

  13. Simplified13.8

    \[\leadsto \frac{1 - {\left(\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}^{3}}{\color{blue}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}}\]
  14. Using strategy rm

  15. Applied add-sqr-sqrt_binary64_214613.8

    \[\leadsto \frac{1 - {\color{blue}{\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}} \cdot \sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}}^{3}}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

  16. Applied unpow-prod-down_binary64_220313.8

    \[\leadsto \frac{1 - \color{blue}{{\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3} \cdot {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}}}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

  17. Applied add-sqr-sqrt_binary64_214613.8

    \[\leadsto \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}} - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3} \cdot {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

  18. Applied difference-of-squares_binary64_209313.8

    \[\leadsto \frac{\color{blue}{\left(\sqrt{1} + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right) \cdot \left(\sqrt{1} - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

  19. Simplified13.8

    \[\leadsto \frac{\color{blue}{\left(1 + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)} \cdot \left(\sqrt{1} - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

  20. Simplified13.8

    \[\leadsto \frac{\left(1 + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right) \cdot \color{blue}{\left(1 - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)} \cdot 1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

  21. Simplified13.8

    \[\leadsto \color{blue}{\frac{\left(1 + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right) \cdot \left(1 - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}}\]

  22. Final simplification13.8

    \[\leadsto \frac{\left(1 + {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right) \cdot \left(1 - {\left(\sqrt{\frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}}\right)}^{3}\right)}{1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}} \cdot \left(1 + \frac{\frac{\left(0.254829592 + \frac{-0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right) + \frac{\frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1 - 0.3275911 \cdot \left|x\right|}{1 - x \cdot \left(x \cdot 0.10731592879921002\right)}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{{\left(e^{x}\right)}^{x}}\right)}\]

Reproduce

herbie shell --seed 2021044 
(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)))))))