Jmat.Real.erf

Average Error: 13.4 → 0.2

Time: 19.4s

Precision: binary64

Cost: 215556

Math

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

↓

\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := {\left(e^{x}\right)}^{x}\\ t_2 := \frac{-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {t_0}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {t_0}^{-3}, \frac{1.421413741}{t_0}\right)}{t_0}}{t_0 \cdot t_1}\\ t_3 := 1 - t_2\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 - {t_2}^{2}}{t_3}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - {\left(-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-3}, \frac{1.421413741}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}^{2} \cdot {\left(\frac{\frac{1}{t_1}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}^{2}}{t_3}\\ \end{array} \]

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 (pow (exp x) x))
        (t_2
         (/
          (+
           -0.254829592
           (/
            (-
             (fma 1.453152027 (pow t_0 -2.0) 0.284496736)
             (fma 1.061405429 (pow t_0 -3.0) (/ 1.421413741 t_0)))
            t_0))
          (* t_0 t_1)))
        (t_3 (- 1.0 t_2)))
   (if (<= x -7.2e-7)
     (/ (- 1.0 (pow t_2 2.0)) t_3)
     (if (<= x 1.2e-6)
       (+ 1e-9 (sqrt (* (* x x) 1.2732557730789702)))
       (/
        (-
         1.0
         (*
          (pow
           (+
            -0.254829592
            (/
             (-
              (fma 1.453152027 (pow (fma 0.3275911 x 1.0) -2.0) 0.284496736)
              (fma
               1.061405429
               (pow (fma 0.3275911 x 1.0) -3.0)
               (/ 1.421413741 (fma 0.3275911 x 1.0))))
             (fma 0.3275911 x 1.0)))
           2.0)
          (pow (/ (/ 1.0 t_1) (fma 0.3275911 x 1.0)) 2.0)))
        t_3)))))

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 = pow(exp(x), x);
	double t_2 = (-0.254829592 + ((fma(1.453152027, pow(t_0, -2.0), 0.284496736) - fma(1.061405429, pow(t_0, -3.0), (1.421413741 / t_0))) / t_0)) / (t_0 * t_1);
	double t_3 = 1.0 - t_2;
	double tmp;
	if (x <= -7.2e-7) {
		tmp = (1.0 - pow(t_2, 2.0)) / t_3;
	} else if (x <= 1.2e-6) {
		tmp = 1e-9 + sqrt(((x * x) * 1.2732557730789702));
	} else {
		tmp = (1.0 - (pow((-0.254829592 + ((fma(1.453152027, pow(fma(0.3275911, x, 1.0), -2.0), 0.284496736) - fma(1.061405429, pow(fma(0.3275911, x, 1.0), -3.0), (1.421413741 / fma(0.3275911, x, 1.0)))) / fma(0.3275911, x, 1.0))), 2.0) * pow(((1.0 / t_1) / fma(0.3275911, x, 1.0)), 2.0))) / t_3;
	}
	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 = exp(x) ^ x
	t_2 = Float64(Float64(-0.254829592 + Float64(Float64(fma(1.453152027, (t_0 ^ -2.0), 0.284496736) - fma(1.061405429, (t_0 ^ -3.0), Float64(1.421413741 / t_0))) / t_0)) / Float64(t_0 * t_1))
	t_3 = Float64(1.0 - t_2)
	tmp = 0.0
	if (x <= -7.2e-7)
		tmp = Float64(Float64(1.0 - (t_2 ^ 2.0)) / t_3);
	elseif (x <= 1.2e-6)
		tmp = Float64(1e-9 + sqrt(Float64(Float64(x * x) * 1.2732557730789702)));
	else
		tmp = Float64(Float64(1.0 - Float64((Float64(-0.254829592 + Float64(Float64(fma(1.453152027, (fma(0.3275911, x, 1.0) ^ -2.0), 0.284496736) - fma(1.061405429, (fma(0.3275911, x, 1.0) ^ -3.0), Float64(1.421413741 / fma(0.3275911, x, 1.0)))) / fma(0.3275911, x, 1.0))) ^ 2.0) * (Float64(Float64(1.0 / t_1) / fma(0.3275911, x, 1.0)) ^ 2.0))) / t_3);
	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[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]}, Block[{t$95$2 = N[(N[(-0.254829592 + N[(N[(N[(1.453152027 * N[Power[t$95$0, -2.0], $MachinePrecision] + 0.284496736), $MachinePrecision] - N[(1.061405429 * N[Power[t$95$0, -3.0], $MachinePrecision] + N[(1.421413741 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 - t$95$2), $MachinePrecision]}, If[LessEqual[x, -7.2e-7], N[(N[(1.0 - N[Power[t$95$2, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[x, 1.2e-6], N[(1e-9 + N[Sqrt[N[(N[(x * x), $MachinePrecision] * 1.2732557730789702), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(N[Power[N[(-0.254829592 + N[(N[(N[(1.453152027 * N[Power[N[(0.3275911 * x + 1.0), $MachinePrecision], -2.0], $MachinePrecision] + 0.284496736), $MachinePrecision] - N[(1.061405429 * N[Power[N[(0.3275911 * x + 1.0), $MachinePrecision], -3.0], $MachinePrecision] + N[(1.421413741 / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[Power[N[(N[(1.0 / t$95$1), $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999989e-7

   1. Initial program 0.2

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

   2. Simplified 0.2

      \[\leadsto \color{blue}{1 + \frac{\frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}} \]
      Proof
      (+.f64 1 (/.f64 (/.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))) (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 (-.f64 (Rewrite<= metadata-eval (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (pow.f64 (exp.f64 x) x))): 1 points increase in error, 0 points decrease in error
      (+.f64 1 (/.f64 (/.f64 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (pow.f64 (exp.f64 x) x))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (/.f64 (/.f64 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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)))) (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 (-.f64 (neg.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)))))) (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 (-.f64 (neg.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))))))))) (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 (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 31853699/125000000) (neg.f64 (*.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)))))))))) (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 (Rewrite<= distribute-neg-in_binary64 (neg.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)))))))))) (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 (neg.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))))))))) (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 (neg.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))))))))) (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 (neg.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))))))))) (+.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 (neg.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))))))))) (+.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 (/.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (neg.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))))))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (neg.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))))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.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, 0 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (neg.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 (neg.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))))))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (*.f64 (neg.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))))))): 2 points increase in error, 1 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.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))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in x around 0 0.2

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

   4. Taylor expanded in x around inf 0.2

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

   5. Applied egg-rr 0.2

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

   6. Simplified 0.2

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

   if -7.19999999999999989e-7 < x < 1.1999999999999999e-6

   1. Initial program 27.1

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

   2. Simplified 27.1

      \[\leadsto \color{blue}{1 + \frac{\frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}} \]
      Proof
      (+.f64 1 (/.f64 (/.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))) (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 (-.f64 (Rewrite<= metadata-eval (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (pow.f64 (exp.f64 x) x))): 1 points increase in error, 0 points decrease in error
      (+.f64 1 (/.f64 (/.f64 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (pow.f64 (exp.f64 x) x))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (/.f64 (/.f64 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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)))) (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 (-.f64 (neg.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)))))) (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 (-.f64 (neg.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))))))))) (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 (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 31853699/125000000) (neg.f64 (*.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)))))))))) (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 (Rewrite<= distribute-neg-in_binary64 (neg.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)))))))))) (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 (neg.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))))))))) (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 (neg.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))))))))) (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 (neg.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))))))))) (+.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 (neg.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))))))))) (+.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 (/.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (neg.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))))))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (neg.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))))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.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, 0 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (neg.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 (neg.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))))))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (*.f64 (neg.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))))))): 2 points increase in error, 1 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.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))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 27.4

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}} \]

   4. Simplified 27.4

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\right)}} \]
      Proof
      (exp.f64 (log1p.f64 (/.f64 (-.f64 -31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (*.f64 (exp.f64 (*.f64 x x)) (fma.f64 3275911/10000000 x 1))))): 0 points increase in error, 0 points decrease in error
      (exp.f64 (log1p.f64 (/.f64 (-.f64 -31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (*.f64 (Rewrite=> exp-prod_binary64 (pow.f64 (exp.f64 x) x)) (fma.f64 3275911/10000000 x 1))))): 0 points increase in error, 0 points decrease in error
      (exp.f64 (log1p.f64 (/.f64 (-.f64 -31853699/125000000 (/.f64 (+.f64 -8890523/31250000 (/.f64 (+.f64 1421413741/1000000000 (/.f64 (+.f64 -1453152027/1000000000 (/.f64 1061405429/1000000000 (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (fma.f64 3275911/10000000 x 1))) (Rewrite<= *-commutative_binary64 (*.f64 (fma.f64 3275911/10000000 x 1) (pow.f64 (exp.f64 x) x)))))): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in x around 0 1.1

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

   6. Simplified 1.1

      \[\leadsto \color{blue}{10^{-9} + x \cdot 1.128386358070218} \]
      Proof
      (+.f64 1/1000000000 (*.f64 x 564193179035109/500000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 1/1000000000 (Rewrite<= *-commutative_binary64 (*.f64 564193179035109/500000000000000 x))): 0 points increase in error, 0 points decrease in error

   7. Applied egg-rr 1.7

      \[\leadsto 10^{-9} + \color{blue}{\left(\left(1 + x \cdot 1.128386358070218\right) - 1\right)} \]

   8. Applied egg-rr 0.2

      \[\leadsto 10^{-9} + \color{blue}{{\left(\left(x \cdot x\right) \cdot 1.2732557730789702\right)}^{0.5}} \]

   9. Simplified 0.2

      \[\leadsto 10^{-9} + \color{blue}{\sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}} \]
      Proof
      (sqrt.f64 (*.f64 (*.f64 x x) 318313943269742557644254641881/250000000000000000000000000000)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unpow1/2_binary64 (pow.f64 (*.f64 (*.f64 x x) 318313943269742557644254641881/250000000000000000000000000000) 1/2)): 0 points increase in error, 0 points decrease in error

   if 1.1999999999999999e-6 < x

   1. Initial program 0.2

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

   2. Simplified 0.2

      \[\leadsto \color{blue}{1 + \frac{\frac{-0.254829592 - \frac{-0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}} \]
      Proof
      (+.f64 1 (/.f64 (/.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))) (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 (-.f64 (Rewrite<= metadata-eval (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (pow.f64 (exp.f64 x) x))): 1 points increase in error, 0 points decrease in error
      (+.f64 1 (/.f64 (/.f64 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (pow.f64 (exp.f64 x) x))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (/.f64 (/.f64 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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))) (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 (-.f64 (neg.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)))) (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 (-.f64 (neg.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)))))) (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 (-.f64 (neg.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))))))))) (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 (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 31853699/125000000) (neg.f64 (*.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)))))))))) (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 (Rewrite<= distribute-neg-in_binary64 (neg.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)))))))))) (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 (neg.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))))))))) (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 (neg.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))))))))) (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 (neg.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))))))))) (+.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 (neg.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))))))))) (+.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 (/.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (neg.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))))))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (neg.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))))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.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, 0 points decrease in error
      (+.f64 1 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (neg.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 (neg.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))))))): 1 points increase in error, 1 points decrease in error
      (+.f64 1 (*.f64 (neg.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))))))): 2 points increase in error, 1 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.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))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in x around 0 0.2

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

   4. Taylor expanded in x around inf 0.2

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

   5. Applied egg-rr 0.2

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

   6. Simplified 0.2

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

   7. Applied egg-rr 0.2

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

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{1 - {\left(\frac{-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{2}}{1 - \frac{-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\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}}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - {\left(-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-3}, \frac{1.421413741}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}^{2} \cdot {\left(\frac{\frac{1}{{\left(e^{x}\right)}^{x}}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}^{2}}{1 - \frac{-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\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}}}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.2
Cost	190280

\[\begin{array}{l} t_0 := {\left(e^{x}\right)}^{x}\\ t_1 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_2 := \frac{-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {t_1}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {t_1}^{-3}, \frac{1.421413741}{t_1}\right)}{t_1}}{t_1 \cdot t_0}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;e^{\mathsf{log1p}\left(t_2\right)}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - {\left(-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-3}, \frac{1.421413741}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}^{2} \cdot {\left(\frac{\frac{1}{t_0}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}^{2}}{1 - t_2}\\ \end{array} \]

Alternative 2
Error	0.2
Cost	117252

\[\begin{array}{l} t_0 := {\left(e^{x}\right)}^{x}\\ t_1 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;e^{\mathsf{log1p}\left(\frac{-0.254829592 + \frac{\mathsf{fma}\left(1.453152027, {t_1}^{-2}, 0.284496736\right) - \mathsf{fma}\left(1.061405429, {t_1}^{-3}, \frac{1.421413741}{t_1}\right)}{t_1}}{t_1 \cdot t_0}\right)}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \frac{0.284496736 + \frac{\frac{1.453152027}{\mathsf{fma}\left(0.3275911, x, 1\right)} - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-2}, 1.421413741\right)}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\frac{\left(x \cdot 0.3275911\right) \cdot \left(x \cdot 0.3275911\right) + -1}{x \cdot 0.3275911 + -1}}}{t_0 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]

Alternative 3
Error	0.2
Cost	67332

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := {\left(e^{x}\right)}^{x}\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;1 + \frac{\frac{-0.254829592 + \frac{\left(0.284496736 + 1.453152027 \cdot \frac{1}{{t_0}^{2}}\right) + \left(1.061405429 \cdot \frac{-1}{{t_0}^{3}} + 1.421413741 \cdot \frac{-1}{t_0}\right)}{t_0}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{t_1}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \frac{0.284496736 + \frac{\frac{1.453152027}{\mathsf{fma}\left(0.3275911, x, 1\right)} - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-2}, 1.421413741\right)}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\frac{\left(x \cdot 0.3275911\right) \cdot \left(x \cdot 0.3275911\right) + -1}{x \cdot 0.3275911 + -1}}}{t_1 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]

Alternative 4
Error	0.2
Cost	54344

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 - t_1 \cdot \left(1.421413741 + t_1 \cdot \left(-1.453152027 + \frac{1.061405429}{t_0}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 - \frac{-0.284496736 + \frac{\mathsf{fma}\left(1.061405429, {\left(\frac{\left(x \cdot 0.3275911\right) \cdot \left(x \cdot 0.3275911\right) + -1}{x \cdot 0.3275911 + -1}\right)}^{-2}, 1.421413741\right) + \frac{-1.453152027}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]

Alternative 5
Error	0.2
Cost	54344

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 - t_1 \cdot \left(1.421413741 + t_1 \cdot \left(-1.453152027 + \frac{1.061405429}{t_0}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \frac{0.284496736 + \frac{\frac{1.453152027}{\mathsf{fma}\left(0.3275911, x, 1\right)} - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{-2}, 1.421413741\right)}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\frac{\left(x \cdot 0.3275911\right) \cdot \left(x \cdot 0.3275911\right) + -1}{x \cdot 0.3275911 + -1}}}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]

Alternative 6
Error	0.2
Cost	53640

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 - t_1 \cdot \left(1.421413741 + t_1 \cdot \left(-1.453152027 + \frac{1.061405429}{t_0}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \frac{0.284496736 + \frac{\frac{1.453152027}{\mathsf{fma}\left(x, 0.3275911, 1\right)} - \mathsf{fma}\left(1.061405429, {\left(\mathsf{fma}\left(x, 0.3275911, 1\right)\right)}^{-2}, 1.421413741\right)}{\mathsf{fma}\left(x, 0.3275911, 1\right)}}{\mathsf{fma}\left(x, 0.3275911, 1\right)}}{\mathsf{fma}\left(x, 0.3275911, 1\right) \cdot e^{x \cdot x}}\\ \end{array} \]

Alternative 7
Error	0.2
Cost	41988

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ t_2 := e^{x \cdot \left(-x\right)}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;1 + t_1 \cdot \left(t_2 \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 - t_1 \cdot \left(1.421413741 + t_1 \cdot \left(-1.453152027 + \frac{1.061405429}{t_0}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-7}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(t_2 \cdot \left(0.254829592 + t_1 \cdot \left(-0.284496736 + t_1 \cdot \left(1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right) \cdot \frac{-1}{t_0}\\ \end{array} \]

Alternative 8
Error	0.3
Cost	41736

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -0.88:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-7}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(e^{x \cdot \left(-x\right)} \cdot \left(0.254829592 + t_1 \cdot \left(-0.284496736 + t_1 \cdot \left(1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right) \cdot \frac{-1}{t_0}\\ \end{array} \]

Alternative 9
Error	0.3
Cost	29320

\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{1 + x \cdot 0.3275911}\\ \mathbf{if}\;x \leq -0.88:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(e^{x \cdot \left(-x\right)} \cdot \left(0.254829592 + t_1 \cdot \left(-0.284496736 + \frac{1}{t_0} \cdot \left(1.421413741 + \left(-1.453152027 + \frac{1.061405429}{t_0}\right) \cdot t_1\right)\right)\right)\right) \cdot \frac{-1}{t_0}\\ \end{array} \]

Alternative 10
Error	0.5
Cost	7112

\[\begin{array}{l} \mathbf{if}\;x \leq -0.88:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{\left(x \cdot x\right) \cdot 1.2732557730789702}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11
Error	0.9
Cost	1224

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

Alternative 12
Error	1.3
Cost	840

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

Alternative 13
Error	1.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + x \cdot 1.128386358070218\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Error	1.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Error	29.9
Cost	64

\[10^{-9} \]

Reproduce

herbie shell --seed 2022330 
(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)))))))