?

Average Accuracy: 79.2% → 99.7%
Time: 33.0s
Precision: binary64
Cost: 277828

?

\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
↓
\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := {t_0}^{2}\\ t_2 := 1 + 0.3275911 \cdot \left|x\right|\\ t_3 := \frac{1.061405429}{t_2}\\ t_4 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + t_3}{t_2}}{t_2}}{t_2}\\ t_5 := t_2 \cdot {\left(e^{x}\right)}^{x}\\ t_6 := \frac{t_4}{t_5}\\ t_7 := {t_6}^{4}\\ t_8 := 1 + \frac{\frac{t_4}{t_2}}{e^{x \cdot x}}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{\frac{1 - {t_7}^{3}}{1 + \left(t_7 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot {t_2}^{-2} + -2.111650813574209}{t_3 + 1.453152027}}{t_2}}{t_2}}{t_2}}{t_5}\right)}^{8}\right)}}{1 + {t_6}^{2}}}{t_8}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{\frac{{\left(\left(0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \left(\frac{1.421413741}{t_1} + \frac{-0.284496736}{t_0}\right)\right)\right) + \frac{-1.453152027}{{t_0}^{3}}\right)}^{2}}{t_1}}{{\left(e^{x}\right)}^{\left(x \cdot 2\right)}}}{t_8}\\ \end{array} \]
(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
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0))
        (t_1 (pow t_0 2.0))
        (t_2 (+ 1.0 (* 0.3275911 (fabs x))))
        (t_3 (/ 1.061405429 t_2))
        (t_4
         (+
          0.254829592
          (/
           (+
            -0.284496736
            (/ (+ 1.421413741 (/ (+ -1.453152027 t_3) t_2)) t_2))
           t_2)))
        (t_5 (* t_2 (pow (exp x) x)))
        (t_6 (/ t_4 t_5))
        (t_7 (pow t_6 4.0))
        (t_8 (+ 1.0 (/ (/ t_4 t_2) (exp (* x x))))))
   (if (<= x -7.6e-7)
     (/
      (/
       (/
        (- 1.0 (pow t_7 3.0))
        (+
         1.0
         (+
          t_7
          (pow
           (/
            (+
             0.254829592
             (/
              (+
               -0.284496736
               (/
                (+
                 1.421413741
                 (/
                  (/
                   (+ (* 1.126581484710674 (pow t_2 -2.0)) -2.111650813574209)
                   (+ t_3 1.453152027))
                  t_2))
                t_2))
              t_2))
            t_5)
           8.0))))
       (+ 1.0 (pow t_6 2.0)))
      t_8)
     (if (<= x 2.5e-6)
       (+ 1e-9 (sqrt (* (* x x) 1.2732557730789702)))
       (/
        (-
         1.0
         (/
          (/
           (pow
            (+
             (+
              0.254829592
              (+
               (/ 1.061405429 (pow t_0 4.0))
               (+ (/ 1.421413741 t_1) (/ -0.284496736 t_0))))
             (/ -1.453152027 (pow t_0 3.0)))
            2.0)
           t_1)
          (pow (exp x) (* x 2.0))))
        t_8)))))
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) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	double t_1 = pow(t_0, 2.0);
	double t_2 = 1.0 + (0.3275911 * fabs(x));
	double t_3 = 1.061405429 / t_2;
	double t_4 = 0.254829592 + ((-0.284496736 + ((1.421413741 + ((-1.453152027 + t_3) / t_2)) / t_2)) / t_2);
	double t_5 = t_2 * pow(exp(x), x);
	double t_6 = t_4 / t_5;
	double t_7 = pow(t_6, 4.0);
	double t_8 = 1.0 + ((t_4 / t_2) / exp((x * x)));
	double tmp;
	if (x <= -7.6e-7) {
		tmp = (((1.0 - pow(t_7, 3.0)) / (1.0 + (t_7 + pow(((0.254829592 + ((-0.284496736 + ((1.421413741 + ((((1.126581484710674 * pow(t_2, -2.0)) + -2.111650813574209) / (t_3 + 1.453152027)) / t_2)) / t_2)) / t_2)) / t_5), 8.0)))) / (1.0 + pow(t_6, 2.0))) / t_8;
	} else if (x <= 2.5e-6) {
		tmp = 1e-9 + sqrt(((x * x) * 1.2732557730789702));
	} else {
		tmp = (1.0 - ((pow(((0.254829592 + ((1.061405429 / pow(t_0, 4.0)) + ((1.421413741 / t_1) + (-0.284496736 / t_0)))) + (-1.453152027 / pow(t_0, 3.0))), 2.0) / t_1) / pow(exp(x), (x * 2.0)))) / t_8;
	}
	return tmp;
}

function code(x)
	return Float64(1.0 - Float64(Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(0.254829592 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(-0.284496736 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(1.421413741 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(-1.453152027 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * 1.061405429))))))))) * exp(Float64(-Float64(abs(x) * abs(x))))))
end
↓
function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = t_0 ^ 2.0
	t_2 = Float64(1.0 + Float64(0.3275911 * abs(x)))
	t_3 = Float64(1.061405429 / t_2)
	t_4 = Float64(0.254829592 + Float64(Float64(-0.284496736 + Float64(Float64(1.421413741 + Float64(Float64(-1.453152027 + t_3) / t_2)) / t_2)) / t_2))
	t_5 = Float64(t_2 * (exp(x) ^ x))
	t_6 = Float64(t_4 / t_5)
	t_7 = t_6 ^ 4.0
	t_8 = Float64(1.0 + Float64(Float64(t_4 / t_2) / exp(Float64(x * x))))
	tmp = 0.0
	if (x <= -7.6e-7)
		tmp = Float64(Float64(Float64(Float64(1.0 - (t_7 ^ 3.0)) / Float64(1.0 + Float64(t_7 + (Float64(Float64(0.254829592 + Float64(Float64(-0.284496736 + Float64(Float64(1.421413741 + Float64(Float64(Float64(Float64(1.126581484710674 * (t_2 ^ -2.0)) + -2.111650813574209) / Float64(t_3 + 1.453152027)) / t_2)) / t_2)) / t_2)) / t_5) ^ 8.0)))) / Float64(1.0 + (t_6 ^ 2.0))) / t_8);
	elseif (x <= 2.5e-6)
		tmp = Float64(1e-9 + sqrt(Float64(Float64(x * x) * 1.2732557730789702)));
	else
		tmp = Float64(Float64(1.0 - Float64(Float64((Float64(Float64(0.254829592 + Float64(Float64(1.061405429 / (t_0 ^ 4.0)) + Float64(Float64(1.421413741 / t_1) + Float64(-0.284496736 / t_0)))) + Float64(-1.453152027 / (t_0 ^ 3.0))) ^ 2.0) / t_1) / (exp(x) ^ Float64(x * 2.0)))) / t_8);
	end
	return tmp
end

code[x_] := N[(1.0 - N[(N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.254829592 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-0.284496736 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.421413741 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.453152027 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.061405429), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[Power[t$95$0, 2.0], $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.061405429 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(0.254829592 + N[(N[(-0.284496736 + N[(N[(1.421413741 + N[(N[(-1.453152027 + t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$4 / t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[Power[t$95$6, 4.0], $MachinePrecision]}, Block[{t$95$8 = N[(1.0 + N[(N[(t$95$4 / t$95$2), $MachinePrecision] / N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.6e-7], N[(N[(N[(N[(1.0 - N[Power[t$95$7, 3.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$7 + N[Power[N[(N[(0.254829592 + N[(N[(-0.284496736 + N[(N[(1.421413741 + N[(N[(N[(N[(1.126581484710674 * N[Power[t$95$2, -2.0], $MachinePrecision]), $MachinePrecision] + -2.111650813574209), $MachinePrecision] / N[(t$95$3 + 1.453152027), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision], 8.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[Power[t$95$6, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$8), $MachinePrecision], If[LessEqual[x, 2.5e-6], N[(1e-9 + N[Sqrt[N[(N[(x * x), $MachinePrecision] * 1.2732557730789702), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(N[(N[Power[N[(N[(0.254829592 + N[(N[(1.061405429 / N[Power[t$95$0, 4.0], $MachinePrecision]), $MachinePrecision] + N[(N[(1.421413741 / t$95$1), $MachinePrecision] + N[(-0.284496736 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.453152027 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / t$95$1), $MachinePrecision] / N[Power[N[Exp[x], $MachinePrecision], N[(x * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$8), $MachinePrecision]]]]]]]]]]]]

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|}
↓
\begin{array}{l}
t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\
t_1 := {t_0}^{2}\\
t_2 := 1 + 0.3275911 \cdot \left|x\right|\\
t_3 := \frac{1.061405429}{t_2}\\
t_4 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + t_3}{t_2}}{t_2}}{t_2}\\
t_5 := t_2 \cdot {\left(e^{x}\right)}^{x}\\
t_6 := \frac{t_4}{t_5}\\
t_7 := {t_6}^{4}\\
t_8 := 1 + \frac{\frac{t_4}{t_2}}{e^{x \cdot x}}\\
\mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\
\;\;\;\;\frac{\frac{\frac{1 - {t_7}^{3}}{1 + \left(t_7 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot {t_2}^{-2} + -2.111650813574209}{t_3 + 1.453152027}}{t_2}}{t_2}}{t_2}}{t_5}\right)}^{8}\right)}}{1 + {t_6}^{2}}}{t_8}\\

\mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\
\;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\

\mathbf{else}:\\
\;\;\;\;\frac{1 - \frac{\frac{{\left(\left(0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \left(\frac{1.421413741}{t_1} + \frac{-0.284496736}{t_0}\right)\right)\right) + \frac{-1.453152027}{{t_0}^{3}}\right)}^{2}}{t_1}}{{\left(e^{x}\right)}^{\left(x \cdot 2\right)}}}{t_8}\\


\end{array}

Error?

Derivation?

  1. Split input into 3 regimes

  2. if x < -7.60000000000000029e-7

    1. Initial program 99.6%

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

    2. Applied egg-rr99.6%

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

      [Start]99.6

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

      flip-- [=>]99.6

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

    3. Applied egg-rr99.6%

      \[\leadsto \frac{\color{blue}{\frac{1 - {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]
      Proof

      [Start]99.6

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

      flip-- [=>]99.6

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

    4. Applied egg-rr99.6%

      \[\leadsto \frac{\frac{\color{blue}{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]
      Proof

      [Start]99.6

      \[ \frac{\frac{1 - {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      flip3-- [=>]99.6

      \[ \frac{\frac{\color{blue}{\frac{{1}^{3} - {\left({\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 {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 \cdot 1 + \left({\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 {\left(e^{x}\right)}^{x}}\right)}^{4} \cdot {\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 {\left(e^{x}\right)}^{x}}\right)}^{4} + 1 \cdot {\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 {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}}}{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 {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

    5. Applied egg-rr99.6%

      \[\leadsto \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\color{blue}{\frac{1.126581484710674 \cdot {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-2} - 2.111650813574209}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]
      Proof

      [Start]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      +-commutative [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\color{blue}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} + -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      flip-+ [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\color{blue}{\frac{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      div-inv [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{\color{blue}{\left(1.061405429 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)} \cdot \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      div-inv [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{\left(1.061405429 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) \cdot \color{blue}{\left(1.061405429 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)} - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      swap-sqr [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{\color{blue}{\left(1.061405429 \cdot 1.061405429\right) \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)} - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      metadata-eval [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{\color{blue}{1.126581484710674} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      inv-pow [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot \left(\color{blue}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1}} \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      inv-pow [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \color{blue}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1}}\right) - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      pow-sqr [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot \color{blue}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{\left(2 \cdot -1\right)}} - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      metadata-eval [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{\color{blue}{-2}} - -1.453152027 \cdot -1.453152027}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      metadata-eval [=>]99.6

      \[ \frac{\frac{\frac{1 - {\left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-2} - \color{blue}{2.111650813574209}}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} - -1.453152027}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{1 + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{\left(1 + 0.3275911 \cdot \left|x\right|\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

    if -7.60000000000000029e-7 < x < 2.5000000000000002e-6

    1. Initial program 57.7%

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

    2. Simplified57.7%

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

      [Start]57.7

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

      associate-*l/ [=>]57.7

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

      *-lft-identity [=>]57.7

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

    3. Applied egg-rr57.3%

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

      [Start]57.7

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

      sub-neg [=>]57.7

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

    4. Simplified57.3%

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

      [Start]57.3

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

      distribute-neg-frac [=>]57.3

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

      *-commutative [=>]57.3

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

      neg-sub0 [=>]57.3

      \[ 1 + \frac{\color{blue}{0 - \left(0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)} \]

      associate--r+ [=>]57.3

      \[ 1 + \frac{\color{blue}{\left(0 - 0.254829592\right) - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)} \]

      metadata-eval [=>]57.3

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

      exp-prod [<=]57.3

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

    5. Taylor expanded in x around 0 98.5%

      \[\leadsto \color{blue}{10^{-9} + 1.128386358070218 \cdot x} \]

    6. Applied egg-rr99.8%

      \[\leadsto 10^{-9} + \color{blue}{\sqrt{1.2732557730789702 \cdot \left(x \cdot x\right)}} \]
      Proof

      [Start]98.5

      \[ 10^{-9} + 1.128386358070218 \cdot x \]

      add-sqr-sqrt [=>]49.8

      \[ 10^{-9} + \color{blue}{\sqrt{1.128386358070218 \cdot x} \cdot \sqrt{1.128386358070218 \cdot x}} \]

      sqrt-unprod [=>]99.8

      \[ 10^{-9} + \color{blue}{\sqrt{\left(1.128386358070218 \cdot x\right) \cdot \left(1.128386358070218 \cdot x\right)}} \]

      swap-sqr [=>]99.8

      \[ 10^{-9} + \sqrt{\color{blue}{\left(1.128386358070218 \cdot 1.128386358070218\right) \cdot \left(x \cdot x\right)}} \]

      metadata-eval [=>]99.8

      \[ 10^{-9} + \sqrt{\color{blue}{1.2732557730789702} \cdot \left(x \cdot x\right)} \]

    if 2.5000000000000002e-6 < x

    1. Initial program 99.8%

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

    2. Applied egg-rr99.8%

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

      [Start]99.8

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

      flip-- [=>]99.8

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

    3. Taylor expanded in x around inf 99.8%

      \[\leadsto \frac{\color{blue}{1 - \frac{{\left(\left(0.254829592 + \left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + 1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)\right)}^{2}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2} \cdot {\left(e^{{x}^{2}}\right)}^{2}}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

    4. Simplified99.8%

      \[\leadsto \frac{\color{blue}{1 - \frac{\frac{{\left(\left(0.254829592 + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \left(\frac{1.421413741}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}} - \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)\right) - \frac{1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}}\right)}^{2}}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}}}{{\left(e^{x}\right)}^{\left(2 \cdot x\right)}}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]
      Proof

      [Start]99.8

      \[ \frac{1 - \frac{{\left(\left(0.254829592 + \left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + 1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)\right)}^{2}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2} \cdot {\left(e^{{x}^{2}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      *-commutative [=>]99.8

      \[ \frac{1 - \frac{{\left(\left(0.254829592 + \left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + 1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)\right)}^{2}}{\color{blue}{{\left(e^{{x}^{2}}\right)}^{2} \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      +-commutative [<=]99.8

      \[ \frac{1 - \frac{{\left(\left(0.254829592 + \left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + 1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)\right)}^{2}}{{\left(e^{{x}^{2}}\right)}^{2} \cdot {\color{blue}{\left(1 + 0.3275911 \cdot \left|x\right|\right)}}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]

      associate-/l/ [<=]99.8

      \[ \frac{1 - \color{blue}{\frac{\frac{{\left(\left(0.254829592 + \left(1.061405429 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + 1.421413741 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(0.284496736 \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 1.453152027 \cdot \frac{1}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right)\right)}^{2}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}}{{\left(e^{{x}^{2}}\right)}^{2}}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification99.7%

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{\frac{1 - {\left({\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 {\left(e^{x}\right)}^{x}}\right)}^{4}\right)}^{3}}{1 + \left({\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 {\left(e^{x}\right)}^{x}}\right)}^{4} + {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{\frac{1.126581484710674 \cdot {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-2} + -2.111650813574209}{\frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|} + 1.453152027}}{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 {\left(e^{x}\right)}^{x}}\right)}^{8}\right)}}{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 {\left(e^{x}\right)}^{x}}\right)}^{2}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{\frac{{\left(\left(0.254829592 + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \left(\frac{1.421413741}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}} + \frac{-0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)\right) + \frac{-1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}}\right)}^{2}}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}}}{{\left(e^{x}\right)}^{\left(x \cdot 2\right)}}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}}{e^{x \cdot x}}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy99.7%
Cost264324
\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := {t_0}^{2}\\ t_2 := 1 + 0.3275911 \cdot \left|x\right|\\ t_3 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_2}}{t_2}}{t_2}}{t_2}\\ t_4 := \frac{t_3}{t_2 \cdot {\left(e^{x}\right)}^{x}}\\ t_5 := {t_4}^{4}\\ t_6 := 1 + \frac{\frac{t_3}{t_2}}{e^{x \cdot x}}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{\frac{1 - {t_5}^{3}}{1 + \left(t_5 + {t_4}^{8}\right)}}{1 + {t_4}^{2}}}{t_6}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{\frac{{\left(\left(0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \left(\frac{1.421413741}{t_1} + \frac{-0.284496736}{t_0}\right)\right)\right) + \frac{-1.453152027}{{t_0}^{3}}\right)}^{2}}{t_1}}{{\left(e^{x}\right)}^{\left(x \cdot 2\right)}}}{t_6}\\ \end{array} \]
Alternative 2
Accuracy99.7%
Cost153032
\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := 1 + 0.3275911 \cdot \left|x\right|\\ t_2 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_1}}{t_1}}{t_1}}{t_1}\\ t_3 := \frac{t_2}{t_1 \cdot {\left(e^{x}\right)}^{x}}\\ t_4 := {t_0}^{2}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;e^{\log \left(\frac{1 - {t_3}^{2}}{1 + t_3}\right)}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{\frac{{\left(\left(0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \left(\frac{1.421413741}{t_4} + \frac{-0.284496736}{t_0}\right)\right)\right) + \frac{-1.453152027}{{t_0}^{3}}\right)}^{2}}{t_4}}{{\left(e^{x}\right)}^{\left(x \cdot 2\right)}}}{1 + \frac{\frac{t_2}{t_1}}{e^{x \cdot x}}}\\ \end{array} \]
Alternative 3
Accuracy99.7%
Cost150088
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}\\ t_2 := t_0 \cdot {\left(e^{x}\right)}^{x}\\ t_3 := \frac{t_1}{t_2}\\ t_4 := \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{t_0}}{t_0}}{t_0}}{t_0}}{t_2}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;e^{\log \left(\frac{1 - {t_3}^{2}}{1 + t_3}\right)}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 - {t_4}^{4}}{1 + {t_4}^{2}}}{1 + \frac{\frac{t_1}{t_0}}{e^{x \cdot x}}}\\ \end{array} \]
Alternative 4
Accuracy99.7%
Cost149960
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}\\ t_2 := t_0 \cdot {\left(e^{x}\right)}^{x}\\ t_3 := \frac{t_1}{t_2}\\ t_4 := {t_3}^{2}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;e^{\log \left(\frac{1 - t_4}{1 + t_3}\right)}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 - {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{t_0}}{t_0}}{t_0}}{t_0}}{t_2}\right)}^{4}}{1 + t_4}}{1 + \frac{\frac{t_1}{t_0}}{e^{x \cdot x}}}\\ \end{array} \]
Alternative 5
Accuracy99.7%
Cost114692
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}}{t_0 \cdot {\left(e^{x}\right)}^{x}}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;e^{\log \left(\frac{1 - {t_1}^{2}}{1 + t_1}\right)}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 6
Accuracy99.7%
Cost108484
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := e^{x \cdot x}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{e^{\log \left(1 - {\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}}{t_0 \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}\right)}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{t_0}}{t_0}}{t_0}}{t_0}}{t_0}}{t_1}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{t_1 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 7
Accuracy99.7%
Cost108356
\[\begin{array}{l} t_0 := e^{x \cdot x}\\ t_1 := 1 + 0.3275911 \cdot \left|x\right|\\ t_2 := 0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_1}}{t_1}}{t_1}}{t_1}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{e^{\log \left(1 - {\left(\frac{t_2}{t_1 \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}\right)}}{1 + \frac{\frac{t_2}{t_1}}{t_0}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{t_0 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 8
Accuracy99.7%
Cost89348
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := e^{x \cdot x}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 - {\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}}{t_0}}{t_1}\right)}^{2}}{1 + \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{t_0}}{t_0}}{t_0}}{t_0}}{t_0}}{t_1}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{t_1 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 9
Accuracy99.7%
Cost89220
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := e^{x \cdot x}\\ t_2 := \frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}}{t_0}}{t_1}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 - {t_2}^{2}}{1 + t_2}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{t_1 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 10
Accuracy99.7%
Cost47748
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}}{t_0 \cdot {\left(e^{x}\right)}^{x}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 11
Accuracy99.7%
Cost41988
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 - t_1 \cdot \left(1.421413741 + \left(-1.453152027 + \frac{1.061405429}{t_0}\right) \cdot t_1\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 12
Accuracy99.7%
Cost41412
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := e^{x \cdot x}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;1 + \frac{\frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t_0}}{t_0}}{t_0}}{t_0}}{t_0}}{t_1}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{t_1 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 13
Accuracy99.5%
Cost41032
\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + 1.061405429 \cdot \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 14
Accuracy99.5%
Cost40904
\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 15
Accuracy99.3%
Cost7112
\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 16
Accuracy98.5%
Cost840
\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + x \cdot \left(1.128386358070218 + x \cdot -0.00011824294398844343\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 17
Accuracy98.4%
Cost584
\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + x \cdot 1.128386358070218\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 18
Accuracy97.5%
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 19
Accuracy53.1%
Cost64
\[10^{-9} \]

Error

Reproduce?

herbie shell --seed 2023143 
(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)))))))