Jmat.Real.erf

Average Error: 13.5 → 0.4

Time: 23.1s

Precision: binary64

Cost: 314436

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := \frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {t_0}^{-4}, 1.421413741 \cdot {t_0}^{-2}\right) - \mathsf{fma}\left(1.453152027, {t_0}^{-3}, \frac{0.284496736}{t_0}\right)\right)}{\frac{t_0}{e^{x \cdot \left(-x\right)}}}\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1 - e^{3 \cdot \left(\log \left(\frac{0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \left(\frac{1.421413741}{{t_0}^{2}} + \left(\frac{-1.453152027}{{t_0}^{3}} + \frac{-0.284496736}{t_0}\right)\right)\right)}{t_0}\right) - x \cdot x\right)}}{1 + \left(t_1 + {t_1}^{2}\right)}\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

FPCore

(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
         (/
          (+
           0.254829592
           (-
            (fma 1.061405429 (pow t_0 -4.0) (* 1.421413741 (pow t_0 -2.0)))
            (fma 1.453152027 (pow t_0 -3.0) (/ 0.284496736 t_0))))
          (/ t_0 (exp (* x (- x)))))))
   (if (<= x -2.4e-17)
     (/
      (-
       1.0
       (exp
        (*
         3.0
         (-
          (log
           (/
            (+
             0.254829592
             (+
              (/ 1.061405429 (pow t_0 4.0))
              (+
               (/ 1.421413741 (pow t_0 2.0))
               (+ (/ -1.453152027 (pow t_0 3.0)) (/ -0.284496736 t_0)))))
            t_0))
          (* x x)))))
      (+ 1.0 (+ t_1 (pow t_1 2.0))))
     (if (<= x 0.00068)
       (sqrt
        (pow
         (+
          1e-9
          (fma
           x
           1.128386358070218
           (fma
            -0.37545125292247583
            (pow x 3.0)
            (* (* x x) -0.00011824294398844343))))
         2.0))
       (pow
        (pow
         (+
          1.0
          (/
           (+
            -0.254829592
            (/
             (-
              0.284496736
              (/
               (pow
                (sqrt
                 (+
                  1.421413741
                  (/
                   (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 x 1.0)))
                   (fma 0.3275911 x 1.0))))
                2.0)
               (fma 0.3275911 x 1.0)))
             (fma 0.3275911 x 1.0)))
           (* (fma 0.3275911 x 1.0) (pow (exp x) x))))
         3.0)
        0.3333333333333333)))))

C

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 = (0.254829592 + (fma(1.061405429, pow(t_0, -4.0), (1.421413741 * pow(t_0, -2.0))) - fma(1.453152027, pow(t_0, -3.0), (0.284496736 / t_0)))) / (t_0 / exp((x * -x)));
	double tmp;
	if (x <= -2.4e-17) {
		tmp = (1.0 - exp((3.0 * (log(((0.254829592 + ((1.061405429 / pow(t_0, 4.0)) + ((1.421413741 / pow(t_0, 2.0)) + ((-1.453152027 / pow(t_0, 3.0)) + (-0.284496736 / t_0))))) / t_0)) - (x * x))))) / (1.0 + (t_1 + pow(t_1, 2.0)));
	} else if (x <= 0.00068) {
		tmp = sqrt(pow((1e-9 + fma(x, 1.128386358070218, fma(-0.37545125292247583, pow(x, 3.0), ((x * x) * -0.00011824294398844343)))), 2.0));
	} else {
		tmp = pow(pow((1.0 + ((-0.254829592 + ((0.284496736 - (pow(sqrt((1.421413741 + ((-1.453152027 + (1.061405429 / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0)))), 2.0) / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0))) / (fma(0.3275911, x, 1.0) * pow(exp(x), x)))), 3.0), 0.3333333333333333);
	}
	return tmp;
}

Julia

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 = Float64(Float64(0.254829592 + Float64(fma(1.061405429, (t_0 ^ -4.0), Float64(1.421413741 * (t_0 ^ -2.0))) - fma(1.453152027, (t_0 ^ -3.0), Float64(0.284496736 / t_0)))) / Float64(t_0 / exp(Float64(x * Float64(-x)))))
	tmp = 0.0
	if (x <= -2.4e-17)
		tmp = Float64(Float64(1.0 - exp(Float64(3.0 * Float64(log(Float64(Float64(0.254829592 + Float64(Float64(1.061405429 / (t_0 ^ 4.0)) + Float64(Float64(1.421413741 / (t_0 ^ 2.0)) + Float64(Float64(-1.453152027 / (t_0 ^ 3.0)) + Float64(-0.284496736 / t_0))))) / t_0)) - Float64(x * x))))) / Float64(1.0 + Float64(t_1 + (t_1 ^ 2.0))));
	elseif (x <= 0.00068)
		tmp = sqrt((Float64(1e-9 + fma(x, 1.128386358070218, fma(-0.37545125292247583, (x ^ 3.0), Float64(Float64(x * x) * -0.00011824294398844343)))) ^ 2.0));
	else
		tmp = (Float64(1.0 + Float64(Float64(-0.254829592 + Float64(Float64(0.284496736 - Float64((sqrt(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0)))) ^ 2.0) / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0))) / Float64(fma(0.3275911, x, 1.0) * (exp(x) ^ x)))) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

Wolfram

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[(N[(0.254829592 + N[(N[(1.061405429 * N[Power[t$95$0, -4.0], $MachinePrecision] + N[(1.421413741 * N[Power[t$95$0, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(1.453152027 * N[Power[t$95$0, -3.0], $MachinePrecision] + N[(0.284496736 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 / N[Exp[N[(x * (-x)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e-17], N[(N[(1.0 - N[Exp[N[(3.0 * N[(N[Log[N[(N[(0.254829592 + N[(N[(1.061405429 / N[Power[t$95$0, 4.0], $MachinePrecision]), $MachinePrecision] + N[(N[(1.421413741 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-1.453152027 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision] + N[(-0.284496736 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]], $MachinePrecision] - N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$1 + N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00068], N[Sqrt[N[Power[N[(1e-9 + N[(x * 1.128386358070218 + N[(-0.37545125292247583 * N[Power[x, 3.0], $MachinePrecision] + N[(N[(x * x), $MachinePrecision] * -0.00011824294398844343), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision], N[Power[N[Power[N[(1.0 + N[(N[(-0.254829592 + N[(N[(0.284496736 - N[(N[Power[N[Sqrt[N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(0.3275911 * x + 1.0), $MachinePrecision] * N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.39999999999999986e-17

   1. Initial program 1.0

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

   2. Simplified 1.0

      \[\leadsto \color{blue}{1 - \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1.061405429}{1 + 0.3275911 \cdot \left|x\right|}\right)\right)\right)\right) \cdot e^{-x \cdot x}\right)} \]
      Proof
      (-.f64 1 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))))) (exp.f64 (neg.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (/.f64 (Rewrite<= metadata-eval (*.f64 1 1061405429/1000000000)) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))))) (exp.f64 (neg.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))))) (exp.f64 (neg.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (Rewrite=> *-lft-identity_binary64 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))) (exp.f64 (neg.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 2 points decrease in error

   3. Taylor expanded in x around -inf 1.0

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

   4. Applied egg-rr 1.0

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

   5. Simplified 1.0

      \[\leadsto \color{blue}{\frac{1 - {\left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}}\right)}^{3}}{1 + \left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}} + {\left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}}\right)}^{2}\right)}} \]
      Proof
      (/.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (*.f64 x (neg.f64 x))))) 3)) (+.f64 1 (+.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (*.f64 x (neg.f64 x))))) (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (*.f64 x (neg.f64 x))))) 2)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x x)))))) 3)) (+.f64 1 (+.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (*.f64 x (neg.f64 x))))) (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (*.f64 x (neg.f64 x))))) 2)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (neg.f64 (*.f64 x x))))) 3)) (+.f64 1 (+.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x x)))))) (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (*.f64 x (neg.f64 x))))) 2)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (neg.f64 (*.f64 x x))))) 3)) (+.f64 1 (+.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (neg.f64 (*.f64 x x))))) (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x x)))))) 2)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 1 (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (neg.f64 (*.f64 x x))))) 3)) (+.f64 1 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (neg.f64 (*.f64 x x))))) 2) (/.f64 (+.f64 31853699/125000000 (-.f64 (fma.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -4) (*.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -2))) (fma.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) -3) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))))) (/.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (exp.f64 (neg.f64 (*.f64 x x))))))))): 0 points increase in error, 0 points decrease in error

   6. Applied egg-rr 1.0

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

   7. Taylor expanded in x around 0 1.0

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

   8. Simplified 1.0

      \[\leadsto \frac{1 - e^{3 \cdot \left(\color{blue}{\log \left(\frac{0.254829592 + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \left(\frac{1.421413741}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}} - \left(\frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + \frac{1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}}\right)\right)\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)} + \left(-x \cdot x\right)\right)}}{1 + \left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}} + {\left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}}\right)}^{2}\right)} \]
      Proof
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1061405429/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4)))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1421413741/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2)) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 8890523/31250000 1)) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 8890523/31250000 1) (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 8890523/31250000 1) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 (Rewrite<= metadata-eval (*.f64 1453152027/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 3)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 (*.f64 1453152027/1000000000 1) (Rewrite=> cube-mult_binary64 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 2 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite<= unpow2_binary64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (+.f64 31853699/125000000 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 2 points decrease in error
      (log.f64 (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 141 points decrease in error
      (log.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (Rewrite=> *-commutative_binary64 (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))): 0 points increase in error, 0 points decrease in error
      (log.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))): 0 points increase in error, 0 points decrease in error

   if -2.39999999999999986e-17 < x < 6.8e-4

   1. Initial program 27.0

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

   2. Simplified 27.0

      \[\leadsto \color{blue}{1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot {\left(e^{x}\right)}^{x}}} \]
      Proof
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 (Rewrite<= metadata-eval (*.f64 1 1061405429/1000000000)) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 (*.f64 1 1061405429/1000000000) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 (*.f64 1 1061405429/1000000000) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 2 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (*.f64 1 (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (*.f64 1 (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (*.f64 1 (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (*.f64 1 (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite=> times-frac_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (/.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 2 points increase in error, 2 points decrease in error
      (-.f64 1 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) 1)) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (/.f64 1 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 2 points decrease in error
      (-.f64 1 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (Rewrite<= exp-neg_binary64 (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 2 points decrease in error

   3. Applied egg-rr 27.0

      \[\leadsto \color{blue}{{\left({\left(1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}} \]

   4. Taylor expanded in x around 0 2.9

      \[\leadsto {\left({\color{blue}{\left(10^{-9} + \left(-0.00011824294398844343 \cdot {x}^{2} + \left(-0.37545125292247583 \cdot {x}^{3} + 1.128386358070218 \cdot x\right)\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   5. Applied egg-rr 0.2

      \[\leadsto \color{blue}{\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, -0.00011824294398844343 \cdot \left(x \cdot x\right)\right)\right)\right)}^{2}}} \]

   if 6.8e-4 < x

   1. Initial program 0.1

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

   2. Simplified 0.1

      \[\leadsto \color{blue}{1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot {\left(e^{x}\right)}^{x}}} \]
      Proof
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 (Rewrite<= metadata-eval (*.f64 1 1061405429/1000000000)) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 (*.f64 1 1061405429/1000000000) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 (*.f64 1 1061405429/1000000000) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (*.f64 1 (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 2 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (*.f64 1 (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (*.f64 1 (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (*.f64 1 (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (/.f64 (*.f64 1 (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))))) (*.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite=> times-frac_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (/.f64 (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000)))))))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 2 points increase in error, 2 points decrease in error
      (-.f64 1 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) 1)) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (/.f64 1 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 2 points decrease in error
      (-.f64 1 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 31853699/125000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -8890523/31250000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1421413741/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 -1453152027/1000000000 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 1061405429/1000000000))))))))) (Rewrite<= exp-neg_binary64 (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 2 points decrease in error

   3. Applied egg-rr 0.1

      \[\leadsto \color{blue}{{\left({\left(1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}} \]

   4. Applied egg-rr 0.1

      \[\leadsto {\left({\left(1 - \frac{0.254829592 + \frac{-0.284496736 + \frac{\color{blue}{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1 - e^{3 \cdot \left(\log \left(\frac{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}} + \left(\frac{-1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}} + \frac{-0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right) - x \cdot x\right)}}{1 + \left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}} + {\left(\frac{0.254829592 + \left(\mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-4}, 1.421413741 \cdot {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}\right) - \mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)}{\frac{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}{e^{x \cdot \left(-x\right)}}}\right)}^{2}\right)}\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\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)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4
Cost	302852

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_2 := {t_0}^{2}\\ t_3 := 0.254829592 + \left(\mathsf{fma}\left(1.061405429, {t_1}^{-4}, 1.421413741 \cdot {t_1}^{-2}\right) - \mathsf{fma}\left(1.453152027, {t_1}^{-3}, \frac{0.284496736}{t_1}\right)\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{1 - e^{3 \cdot \left(\log \left(\frac{t_3}{t_1}\right) - x \cdot x\right)}}{1 + \left(\frac{t_3}{\frac{t_1}{e^{x \cdot \left(-x\right)}}} + \frac{{\left(\left(0.254829592 + \left(1.061405429 \cdot \frac{1}{{t_0}^{4}} + 1.421413741 \cdot \frac{1}{t_2}\right)\right) + \left(0.284496736 \cdot \frac{-1}{t_0} + -1.453152027 \cdot \frac{1}{{t_0}^{3}}\right)\right)}^{2} \cdot {\left(e^{-{x}^{2}}\right)}^{2}}{t_2}\right)}\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternative 2
Error	0.4
Cost	215940

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := \mathsf{fma}\left(1.061405429, {t_0}^{-4}, 1.421413741 \cdot {t_0}^{-2}\right) - \mathsf{fma}\left(1.453152027, {t_0}^{-3}, \frac{0.284496736}{t_0}\right)\\ t_2 := e^{x \cdot \left(-x\right)}\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{-17}:\\ \;\;\;\;\frac{1 - {\left(\frac{0.254829592 + t_1}{t_0} \cdot t_2\right)}^{2}}{1 - t_2 \cdot \frac{-0.254829592 - t_1}{t_0}}\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternative 3
Error	0.4
Cost	117572

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{-17}:\\ \;\;\;\;\log \left(e^{1 + \frac{-0.254829592 - \left(\mathsf{fma}\left(1.061405429, {t_0}^{-4}, 1.421413741 \cdot {t_0}^{-2}\right) - \mathsf{fma}\left(1.453152027, {t_0}^{-3}, \frac{0.284496736}{t_0}\right)\right)}{\frac{t_0}{e^{x \cdot \left(-x\right)}}}}\right)\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternative 4
Error	0.4
Cost	85956

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\left(\frac{0.284496736}{t_0} + \frac{1.453152027}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}\right) + \left(\frac{-1.061405429}{{t_0}^{4}} + \frac{-1.421413741}{{t_0}^{2}}\right)\right)}{\frac{t_0}{e^{x \cdot \left(-x\right)}}}\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternative 5
Error	0.4
Cost	79620

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := {t_0}^{3}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;1 + \left(e^{x \cdot \left(-x\right)} \cdot \left(0.254829592 + \left(\frac{-1.453152027}{t_1} - \frac{\left(0.284496736 + \frac{-1.421413741}{t_0}\right) - \frac{1.061405429}{t_1}}{t_0}\right)\right)\right) \cdot \frac{-1}{1 + 0.3275911 \cdot \left|x\right|}\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternative 6
Error	0.4
Cost	73032

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 + t_1 \cdot \left(1.453152027 \cdot t_1 + \left(-1.421413741 + 1.061405429 \cdot \frac{-1}{{t_0}^{2}}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.00068:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternative 7
Error	0.4
Cost	48580

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ t_2 := \frac{-1}{t_0}\\ t_3 := e^{x \cdot \left(-x\right)}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;1 + t_1 \cdot \left(t_3 \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 + t_1 \cdot \left(1.453152027 \cdot t_1 + \left(-1.421413741 + 1.061405429 \cdot \frac{-1}{{t_0}^{2}}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.00052:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(t_3 \cdot \left(-0.254829592 - t_2 \cdot \left(0.284496736 - t_2 \cdot \left(-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	0.4
Cost	41988

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := e^{x \cdot \left(-x\right)}\\ t_2 := \frac{-1}{t_0}\\ t_3 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;1 + \left(t_1 \cdot \left(0.254829592 + t_3 \cdot \left(-0.284496736 - t_3 \cdot \left(-1.421413741 - t_2 \cdot \left(1.453152027 + \frac{-1.061405429}{t_0}\right)\right)\right)\right)\right) \cdot t_2\\ \mathbf{elif}\;x \leq 0.00052:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(t_1 \cdot \left(-0.254829592 - t_2 \cdot \left(0.284496736 - t_2 \cdot \left(-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	0.6
Cost	35336

\[\begin{array}{l} t_0 := \frac{-1}{1 + 0.3275911 \cdot \left|x\right|}\\ \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.00052:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 - t_0 \cdot \left(0.284496736 - t_0 \cdot \left(-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	0.6
Cost	33096

\[\begin{array}{l} t_0 := \frac{1}{1 + x \cdot 0.3275911}\\ t_1 := 1 + 0.3275911 \cdot \left|x\right|\\ \mathbf{if}\;x \leq -1.05:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.00052:\\ \;\;\;\;\sqrt{{\left(10^{-9} + \mathsf{fma}\left(x, 1.128386358070218, \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, \left(x \cdot x\right) \cdot -0.00011824294398844343\right)\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1}{t_1} \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_0 \cdot \left(0.284496736 - \frac{-1}{t_1} \cdot \left(-1.421413741 + t_0 \cdot \left(1.453152027 + \frac{-1.061405429}{t_1}\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	0.7
Cost	29320

\[\begin{array}{l} t_0 := \frac{1}{1 + x \cdot 0.3275911}\\ t_1 := 1 + 0.3275911 \cdot \left|x\right|\\ t_2 := 1 + \frac{1}{t_1} \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_0 \cdot \left(0.284496736 - \frac{-1}{t_1} \cdot \left(-1.421413741 + t_0 \cdot \left(1.453152027 + \frac{-1.061405429}{t_1}\right)\right)\right)\right)\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.00052:\\ \;\;\;\;\left(\mathsf{fma}\left(-0.00011824294398844343, x \cdot x, 10^{-9}\right) + x \cdot 1.128386358070218\right) + -0.37545125292247583 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	0.8
Cost	28036

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{-1}{t_0}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-17}:\\ \;\;\;\;1 + \frac{1}{t_0} \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + \left(-0.284496736 + t_1 \cdot -1.029667143\right) \cdot t_1\right)\right)\\ \mathbf{elif}\;x \leq 1.1:\\ \;\;\;\;\left(\mathsf{fma}\left(-0.00011824294398844343, x \cdot x, 10^{-9}\right) + x \cdot 1.128386358070218\right) + -0.37545125292247583 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]

Alternative 13
Error	0.9
Cost	13960

\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 1.1:\\ \;\;\;\;\left(x \cdot x\right) \cdot -0.00011824294398844343 + \left(10^{-9} + \mathsf{fma}\left(-0.37545125292247583, {x}^{3}, x \cdot 1.128386358070218\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]

Alternative 14
Error	0.9
Cost	13960

\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 1.1:\\ \;\;\;\;\left(\mathsf{fma}\left(-0.00011824294398844343, x \cdot x, 10^{-9}\right) + x \cdot 1.128386358070218\right) + -0.37545125292247583 \cdot {x}^{3}\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]

Alternative 15
Error	29.7
Cost	12864

\[\sqrt{\sqrt[3]{10^{-54}}} \]

Alternative 16
Error	29.1
Cost	7816

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-25}:\\ \;\;\;\;{\left( 10^{-27} \right)}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 920000000:\\ \;\;\;\;\frac{10^{-27} + {x}^{3} \cdot 1.436724444676459}{\left(x \cdot x\right) \cdot 1.2732557730789702 + \left(10^{-18} + x \cdot -1.128386358070218 \cdot 10^{-9}\right)}\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 + \sqrt[3]{10^{-27}}\right)\\ \end{array} \]

Alternative 17
Error	1.0
Cost	7816

\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;\frac{10^{-27} + {x}^{3} \cdot 1.436724444676459}{\left(x \cdot x\right) \cdot 1.2732557730789702 + \left(10^{-18} + x \cdot -1.128386358070218 \cdot 10^{-9}\right)}\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]

Alternative 18
Error	29.1
Cost	6984

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-25}:\\ \;\;\;\;{\left( 10^{-27} \right)}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 920000000:\\ \;\;\;\;\frac{10^{-18} + x \cdot \left(x \cdot -1.2732557730789702\right)}{10^{-9} + x \cdot -1.128386358070218}\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 + \sqrt[3]{10^{-27}}\right)\\ \end{array} \]

Alternative 19
Error	29.1
Cost	6728

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-23}:\\ \;\;\;\;\sqrt[3]{10^{-27}}\\ \mathbf{elif}\;x \leq 920000000:\\ \;\;\;\;\frac{10^{-18} + x \cdot \left(x \cdot -1.2732557730789702\right)}{10^{-9} + x \cdot -1.128386358070218}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{10^{-27}}\\ \end{array} \]

Alternative 20
Error	29.1
Cost	6728

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-25}:\\ \;\;\;\;{\left( 10^{-27} \right)}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 920000000:\\ \;\;\;\;\frac{10^{-18} + x \cdot \left(x \cdot -1.2732557730789702\right)}{10^{-9} + x \cdot -1.128386358070218}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{10^{-27}}\\ \end{array} \]

Alternative 21
Error	31.7
Cost	320

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

Reproduce

herbie shell --seed 2022325 
(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)))))))