Average Error: 13.5 → 0.2
Time: 23.1s
Precision: binary64
Cost: 130884
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
↓
\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := \frac{\sqrt{1.421413741}}{t_0}\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;1 - \frac{0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \mathsf{fma}\left(t_1, t_1, -\mathsf{fma}\left(1.453152027, {t_0}^{-3}, \frac{0.284496736}{t_0}\right)\right)\right)}{t_0} \cdot e^{\frac{-1}{{\left(\frac{1}{x}\right)}^{2}}}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
(FPCore (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 (/ (sqrt 1.421413741) t_0)))
   (if (<= x -1.15e-6)
     (-
      1.0
      (*
       (/
        (+
         0.254829592
         (+
          (/ 1.061405429 (pow t_0 4.0))
          (fma
           t_1
           t_1
           (- (fma 1.453152027 (pow t_0 -3.0) (/ 0.284496736 t_0))))))
        t_0)
       (exp (/ -1.0 (pow (/ 1.0 x) 2.0)))))
     (if (<= x 7.8e-6)
       (+
        (sqrt
         (pow (* x (fma x -0.00011824294398844343 1.128386358070218)) 2.0))
        1e-9)
       (pow
        (pow
         (+
          1.0
          (/
           (+
            -0.254829592
            (/
             (-
              0.284496736
              (/
               (pow
                (sqrt
                 (+
                  1.421413741
                  (/
                   (+ -1.453152027 (/ 1.061405429 (fma 0.3275911 x 1.0)))
                   (fma 0.3275911 x 1.0))))
                2.0)
               (fma 0.3275911 x 1.0)))
             (fma 0.3275911 x 1.0)))
           (* (fma 0.3275911 x 1.0) (pow (exp x) x))))
         3.0)
        0.3333333333333333)))))
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 = sqrt(1.421413741) / t_0;
	double tmp;
	if (x <= -1.15e-6) {
		tmp = 1.0 - (((0.254829592 + ((1.061405429 / pow(t_0, 4.0)) + fma(t_1, t_1, -fma(1.453152027, pow(t_0, -3.0), (0.284496736 / t_0))))) / t_0) * exp((-1.0 / pow((1.0 / x), 2.0))));
	} else if (x <= 7.8e-6) {
		tmp = sqrt(pow((x * fma(x, -0.00011824294398844343, 1.128386358070218)), 2.0)) + 1e-9;
	} else {
		tmp = pow(pow((1.0 + ((-0.254829592 + ((0.284496736 - (pow(sqrt((1.421413741 + ((-1.453152027 + (1.061405429 / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0)))), 2.0) / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0))) / (fma(0.3275911, x, 1.0) * pow(exp(x), x)))), 3.0), 0.3333333333333333);
	}
	return tmp;
}

function code(x)
	return Float64(1.0 - Float64(Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(0.254829592 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(-0.284496736 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(1.421413741 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * Float64(-1.453152027 + Float64(Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x)))) * 1.061405429))))))))) * exp(Float64(-Float64(abs(x) * abs(x))))))
end
↓
function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = Float64(sqrt(1.421413741) / t_0)
	tmp = 0.0
	if (x <= -1.15e-6)
		tmp = Float64(1.0 - Float64(Float64(Float64(0.254829592 + Float64(Float64(1.061405429 / (t_0 ^ 4.0)) + fma(t_1, t_1, Float64(-fma(1.453152027, (t_0 ^ -3.0), Float64(0.284496736 / t_0)))))) / t_0) * exp(Float64(-1.0 / (Float64(1.0 / x) ^ 2.0)))));
	elseif (x <= 7.8e-6)
		tmp = Float64(sqrt((Float64(x * fma(x, -0.00011824294398844343, 1.128386358070218)) ^ 2.0)) + 1e-9);
	else
		tmp = (Float64(1.0 + Float64(Float64(-0.254829592 + Float64(Float64(0.284496736 - Float64((sqrt(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0)))) ^ 2.0) / fma(0.3275911, x, 1.0))) / fma(0.3275911, x, 1.0))) / Float64(fma(0.3275911, x, 1.0) * (exp(x) ^ x)))) ^ 3.0) ^ 0.3333333333333333;
	end
	return tmp
end

code[x_] := N[(1.0 - N[(N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.254829592 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-0.284496736 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.421413741 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.453152027 + N[(N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.061405429), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[1.421413741], $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x, -1.15e-6], N[(1.0 - N[(N[(N[(0.254829592 + N[(N[(1.061405429 / N[Power[t$95$0, 4.0], $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$1 + (-N[(1.453152027 * N[Power[t$95$0, -3.0], $MachinePrecision] + N[(0.284496736 / t$95$0), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] * N[Exp[N[(-1.0 / N[Power[N[(1.0 / x), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-6], N[(N[Sqrt[N[Power[N[(x * N[(x * -0.00011824294398844343 + 1.128386358070218), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision] + 1e-9), $MachinePrecision], N[Power[N[Power[N[(1.0 + N[(N[(-0.254829592 + N[(N[(0.284496736 - N[(N[Power[N[Sqrt[N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.3275911 * x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(0.3275911 * x + 1.0), $MachinePrecision] * N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]]]]]

1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\begin{array}{l}
t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\
t_1 := \frac{\sqrt{1.421413741}}{t_0}\\
\mathbf{if}\;x \leq -1.15 \cdot 10^{-6}:\\
\;\;\;\;1 - \frac{0.254829592 + \left(\frac{1.061405429}{{t_0}^{4}} + \mathsf{fma}\left(t_1, t_1, -\mathsf{fma}\left(1.453152027, {t_0}^{-3}, \frac{0.284496736}{t_0}\right)\right)\right)}{t_0} \cdot e^{\frac{-1}{{\left(\frac{1}{x}\right)}^{2}}}\\

\mathbf{elif}\;x \leq 7.8 \cdot 10^{-6}:\\
\;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\

\mathbf{else}:\\
\;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\


\end{array}

Error

Derivation

  1. Split input into 3 regimes

  2. if x < -1.15e-6

    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. Simplified0.2

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

    3. Taylor expanded in x around inf 0.2

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

    4. Simplified0.2

      \[\leadsto \color{blue}{1 - \frac{0.254829592 + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \left(\frac{1.421413741}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}} - \left(\frac{1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}} + \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot e^{\frac{-1}{{\left(\frac{1}{x}\right)}^{2}}}} \]
      Proof
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1061405429/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 4)) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (/.f64 4 2)) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (/.f64 4 2))))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (*.f64 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) (/.f64 4 2)) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (/.f64 4 2)))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (Rewrite=> metadata-eval 2)) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (/.f64 4 2)))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) (/.f64 4 2)))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (Rewrite=> metadata-eval 2)))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (Rewrite<= unpow2_binary64 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2)))) (-.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1421413741/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2)) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1453152027/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 3)) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (Rewrite<= cube-unmult_binary64 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 1 points increase in error, 1 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (Rewrite<= unpow2_binary64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (/.f64 (Rewrite<= metadata-eval (*.f64 8890523/31250000 1)) (fma.f64 3275911/10000000 (fabs.f64 x) 1)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (/.f64 (*.f64 8890523/31250000 1) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (/.f64 (*.f64 8890523/31250000 1) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (Rewrite<= associate-*r/_binary64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 31853699/125000000 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 1 points increase in error, 2 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 139 points increase in error, 2 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (exp.f64 (/.f64 -1 (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) (pow.f64 (/.f64 1 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2)))))))): 0 points increase in error, 3 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= associate--l-_binary64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 3 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2)))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2))) (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (*.f64 8890523/31250000 (/.f64 1 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2)))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 3 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))) (/.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2) 2))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2)))))) (exp.f64 (neg.f64 (/.f64 1 (pow.f64 (/.f64 1 x) 2))))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))): 3 points increase in error, 0 points decrease in error

    5. Applied egg-rr0.2

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

    if -1.15e-6 < x < 7.7999999999999999e-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. Simplified27.0

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

    3. Applied egg-rr27.3

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

    4. Taylor expanded in x around 0 3.6

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

    5. Simplified3.6

      \[\leadsto {\left({\color{blue}{\left(10^{-9} + \mathsf{fma}\left(1.128386358070218, x, x \cdot \left(x \cdot -0.00011824294398844343\right)\right)\right)}}^{3}\right)}^{0.3333333333333333} \]
      Proof
      (+.f64 1/1000000000 (fma.f64 564193179035109/500000000000000 x (*.f64 x (*.f64 x -2364858879768868679/20000000000000000000000)))): 0 points increase in error, 0 points decrease in error
      (+.f64 1/1000000000 (fma.f64 564193179035109/500000000000000 x (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x x) -2364858879768868679/20000000000000000000000)))): 12 points increase in error, 7 points decrease in error
      (+.f64 1/1000000000 (fma.f64 564193179035109/500000000000000 x (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 x 2)) -2364858879768868679/20000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 1/1000000000 (fma.f64 564193179035109/500000000000000 x (Rewrite<= *-commutative_binary64 (*.f64 -2364858879768868679/20000000000000000000000 (pow.f64 x 2))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1/1000000000 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 564193179035109/500000000000000 x) (*.f64 -2364858879768868679/20000000000000000000000 (pow.f64 x 2))))): 2 points increase in error, 0 points decrease in error
      (+.f64 1/1000000000 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -2364858879768868679/20000000000000000000000 (pow.f64 x 2)) (*.f64 564193179035109/500000000000000 x)))): 0 points increase in error, 0 points decrease in error

    6. Applied egg-rr0.9

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

    7. Applied egg-rr0.1

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

    if 7.7999999999999999e-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. Simplified0.2

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

    3. Applied egg-rr0.2

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

    4. Applied egg-rr0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;1 - \frac{0.254829592 + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \mathsf{fma}\left(\frac{\sqrt{1.421413741}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, \frac{\sqrt{1.421413741}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, -\mathsf{fma}\left(1.453152027, {\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{-3}, \frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)\right)\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot e^{\frac{-1}{{\left(\frac{1}{x}\right)}^{2}}}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]

Alternatives

Alternative 1
Error0.2
Cost73032
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := {t_0}^{2}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;1 + \left(\left(0.254829592 + \frac{\left(1.421413741 \cdot \frac{1}{t_0} + 1.061405429 \cdot \frac{1}{t_0 \cdot t_1}\right) + \left(-0.284496736 + 1.453152027 \cdot \frac{-1}{t_1}\right)}{t_0}\right) \cdot e^{x \cdot \left(-x\right)}\right) \cdot \frac{-1}{t_0}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(1 + \frac{-0.254829592 + \frac{0.284496736 - \frac{{\left(\sqrt{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}\right)}^{2}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right) \cdot {\left(e^{x}\right)}^{x}}\right)}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
Alternative 2
Error0.2
Cost61700
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ t_2 := {t_0}^{2}\\ t_3 := e^{x \cdot \left(-x\right)}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;1 + \left(\left(0.254829592 + \frac{\left(1.421413741 \cdot t_1 + 1.061405429 \cdot \frac{1}{t_0 \cdot t_2}\right) + \left(-0.284496736 + 1.453152027 \cdot \frac{-1}{t_2}\right)}{t_0}\right) \cdot t_3\right) \cdot \frac{-1}{t_0}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1 - t_1 \cdot \left(t_3 \cdot \left(0.254829592 + t_1 \cdot \left(-0.284496736 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]
Alternative 3
Error0.2
Cost42116
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := e^{x \cdot \left(-x\right)}\\ t_2 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;1 + t_1 \cdot \left(\left(0.254829592 + t_2 \cdot \left(-0.284496736 + t_2 \cdot \left(1.421413741 + t_2 \cdot \left(-1.453152027 + 1.061405429 \cdot t_2\right)\right)\right)\right) \cdot \frac{-1}{t_0}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1 - t_2 \cdot \left(t_1 \cdot \left(0.254829592 + t_2 \cdot \left(-0.284496736 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]
Alternative 4
Error0.2
Cost41988
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ t_2 := e^{x \cdot \left(-x\right)}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;1 - t_1 \cdot \left(t_2 \cdot \left(0.254829592 + t_1 \cdot \left(-0.284496736 + t_1 \cdot \left(1.421413741 + t_1 \cdot \left(-1.453152027 + \frac{1.061405429}{t_0}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1 - t_1 \cdot \left(t_2 \cdot \left(0.254829592 + t_1 \cdot \left(-0.284496736 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]
Alternative 5
Error0.3
Cost35336
\[\begin{array}{l} t_0 := \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\\ \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1 - t_0 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(0.254829592 + t_0 \cdot \left(-0.284496736 + \frac{1}{1 + x \cdot 0.3275911} \cdot \left(1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)\right)\\ \end{array} \]
Alternative 6
Error0.3
Cost29320
\[\begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ t_1 := \frac{1}{t_0}\\ t_2 := 1 + x \cdot 0.3275911\\ \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + \left(-0.284496736 + t_1 \cdot \left(1.421413741 + \frac{1}{t_2} \cdot \left(-1.453152027 + \frac{1.061405429}{t_0}\right)\right)\right) \cdot \frac{-1}{t_2}\right)\right)\\ \end{array} \]
Alternative 7
Error0.9
Cost19976
\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;\sqrt{{\left(\mathsf{fma}\left(x, 1.128386358070218 + x \cdot -0.00011824294398844343, 10^{-9}\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]
Alternative 8
Error0.5
Cost19976
\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;\sqrt{{\left(x \cdot \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right)\right)}^{2}} + 10^{-9}\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]
Alternative 9
Error1.0
Cost15048
\[\begin{array}{l} t_0 := x \cdot \left(1.128386358070218 + x \cdot -0.00011824294398844343\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;\frac{10^{-27} + {t_0}^{3}}{{t_0}^{2} + \left(10^{-18} + 10^{-9} \cdot \left(x \cdot \left(-1.128386358070218 + x \cdot 0.00011824294398844343\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]
Alternative 10
Error1.0
Cost6792
\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + x \cdot \left(\left(1.2732557730789702 + \left(x \cdot x\right) \cdot -1.3981393803054172 \cdot 10^{-8}\right) \cdot \frac{1}{1.128386358070218 + x \cdot 0.00011824294398844343}\right)\\ \mathbf{else}:\\ \;\;\;\;{1}^{0.3333333333333333}\\ \end{array} \]
Alternative 11
Error29.7
Cost64
\[10^{-9} \]

Error

Reproduce

herbie shell --seed 2022325 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))