Average Error: 14.1 → 13.3
Time: 13.2s
Precision: binary64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{1 - \sqrt{{\left(\frac{0.254829592 + \frac{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}} \cdot \sqrt{{\left(\frac{0.254829592 + \frac{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}^{3}}}{1 + \frac{0.254829592 + \frac{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}} \cdot \left(1 + \frac{0.254829592 + \frac{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot e^{{\left(\left|x\right|\right)}^{2}}}\right)}\]
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{1 - \sqrt{{\left(\frac{0.254829592 + \frac{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{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{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{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{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{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{\left(\frac{1.061405429}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + -0.284496736\right) - \frac{\frac{1.453152027}{1 + 0.3275911 \cdot \left|x\right|} - 1.421413741}{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
   (*
    (sqrt
     (pow
      (/
       (+
        0.254829592
        (/
         (-
          (+
           (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3.0))
           -0.284496736)
          (/
           (- (/ 1.453152027 (+ 1.0 (* 0.3275911 (fabs x)))) 1.421413741)
           (+ 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
      (/
       (+
        0.254829592
        (/
         (-
          (+
           (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3.0))
           -0.284496736)
          (/
           (- (/ 1.453152027 (+ 1.0 (* 0.3275911 (fabs x)))) 1.421413741)
           (+ 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
      (/
       (-
        (+
         (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3.0))
         -0.284496736)
        (/
         (- (/ 1.453152027 (+ 1.0 (* 0.3275911 (fabs x)))) 1.421413741)
         (+ 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
       (/
        (-
         (+
          (/ 1.061405429 (pow (+ 1.0 (* 0.3275911 (fabs x))) 3.0))
          -0.284496736)
         (/
          (- (/ 1.453152027 (+ 1.0 (* 0.3275911 (fabs x)))) 1.421413741)
          (+ 1.0 (* 0.3275911 (fabs x)))))
        (+ 1.0 (* 0.3275911 (fabs x)))))
      (* (+ 1.0 (* 0.3275911 (fabs x))) (exp (pow (fabs x) 2.0)))))))))
double code(double x) {
	return 1.0 - (((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (0.254829592 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-0.284496736 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (1.421413741 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x))));
}
↓
double code(double x) {
	return (1.0 - (sqrt(pow(((0.254829592 + ((((1.061405429 / pow((1.0 + (0.3275911 * fabs(x))), 3.0)) + -0.284496736) - (((1.453152027 / (1.0 + (0.3275911 * fabs(x)))) - 1.421413741) / (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(((0.254829592 + ((((1.061405429 / pow((1.0 + (0.3275911 * fabs(x))), 3.0)) + -0.284496736) - (((1.453152027 / (1.0 + (0.3275911 * fabs(x)))) - 1.421413741) / (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 + ((((1.061405429 / pow((1.0 + (0.3275911 * fabs(x))), 3.0)) + -0.284496736) - (((1.453152027 / (1.0 + (0.3275911 * fabs(x)))) - 1.421413741) / (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 + ((((1.061405429 / pow((1.0 + (0.3275911 * fabs(x))), 3.0)) + -0.284496736) - (((1.453152027 / (1.0 + (0.3275911 * fabs(x)))) - 1.421413741) / (1.0 + (0.3275911 * fabs(x))))) / (1.0 + (0.3275911 * fabs(x))))) / ((1.0 + (0.3275911 * fabs(x))) * exp(pow(fabs(x), 2.0)))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

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

  2. Simplified14.1

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

  3. Taylor expanded around 0 14.1

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

  4. Simplified14.1

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

  6. Applied flip3--_binary6414.1

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

  7. Simplified14.1

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

  8. Simplified14.1

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

  10. Applied add-sqr-sqrt_binary6413.3

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

  11. Final simplification13.3

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

Reproduce

herbie shell --seed 2020220 
(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)))))))