Average Error: 13.9 → 13.9
Time: 31.0s
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{1 - {\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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x}\right)}^{3}}{1 + \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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x} + \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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x}\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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x}\right)\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{1 - {\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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x}\right)}^{3}}{1 + \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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x} + \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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x}\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{\frac{1}{\sqrt[3]{1 + 0.3275911 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911 \cdot \left|x\right|}}}{\sqrt[3]{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^{-x \cdot x}\right)\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
    (*
     (*
      (/ 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
              (*
               (cbrt (+ 1.0 (* 0.3275911 (fabs x))))
               (cbrt (+ 1.0 (* 0.3275911 (fabs x))))))
             (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
            (+
             -1.453152027
             (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))
     (exp (- (* x x))))
    3.0))
  (+
   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
              (*
               (cbrt (+ 1.0 (* 0.3275911 (fabs x))))
               (cbrt (+ 1.0 (* 0.3275911 (fabs x))))))
             (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
            (+
             -1.453152027
             (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))
     (exp (- (* x x))))
    (*
     (*
      (*
       (/ 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
               (*
                (cbrt (+ 1.0 (* 0.3275911 (fabs x))))
                (cbrt (+ 1.0 (* 0.3275911 (fabs x))))))
              (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
             (+
              -1.453152027
              (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))
      (exp (- (* x x))))
     (*
      (*
       (/ 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
               (*
                (cbrt (+ 1.0 (* 0.3275911 (fabs x))))
                (cbrt (+ 1.0 (* 0.3275911 (fabs x))))))
              (cbrt (+ 1.0 (* 0.3275911 (fabs x)))))
             (+
              -1.453152027
              (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))
      (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((((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 / (cbrt(1.0 + (0.3275911 * fabs(x))) * cbrt(1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(x * x))), 3.0)) / (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 / (cbrt(1.0 + (0.3275911 * fabs(x))) * cbrt(1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(x * x))) + ((((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 / (cbrt(1.0 + (0.3275911 * fabs(x))) * cbrt(1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(x * x))) * (((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 / (cbrt(1.0 + (0.3275911 * fabs(x))) * cbrt(1.0 + (0.3275911 * fabs(x))))) / cbrt(1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(x * x))))));
}

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 add-cube-cbrt_binary64_250014.0

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

  4. Applied associate-/r*_binary64_240914.0

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

  5. Simplified14.0

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

  7. Applied flip3--_binary64_246913.9

    \[\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{\frac{1}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{\sqrt[3]{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{\frac{1}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{\sqrt[3]{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{\frac{1}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{\sqrt[3]{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{\frac{1}{\sqrt[3]{1 + \left|x\right| \cdot 0.3275911} \cdot \sqrt[3]{1 + \left|x\right| \cdot 0.3275911}}}{\sqrt[3]{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)}}\]

  8. Final simplification13.9

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

Reproduce

herbie shell --seed 2021024 
(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)))))))