Average Error: 13.6 → 0.4
Time: 14.4s
Precision: binary64
Cost: 98628
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
↓
\[\begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ \mathbf{if}\;\left|x\right| \leq 10^{-8}:\\ \;\;\;\;\frac{\mathsf{fma}\left({x}^{3}, 1.436724444676459, 10^{-27}\right)}{\left(x \cdot x\right) \cdot 1.2732557730789702 + \left(10^{-18} - \sqrt{{\left(x \cdot 1.128386358070218 \cdot 10^{-9}\right)}^{2}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + e^{x \cdot \left(-x\right)} \cdot \frac{\left(\frac{-1.061405429}{{t_0}^{4}} + \frac{-1.421413741}{{t_0}^{2}}\right) - \left(0.254829592 + \left(\frac{-0.284496736}{t_0} + \frac{-1.453152027}{{t_0}^{3}}\right)\right)}{t_0}\\ \end{array} \]
(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)))
   (if (<= (fabs x) 1e-8)
     (/
      (fma (pow x 3.0) 1.436724444676459 1e-27)
      (+
       (* (* x x) 1.2732557730789702)
       (- 1e-18 (sqrt (pow (* x 1.128386358070218e-9) 2.0)))))
     (+
      1.0
      (*
       (exp (* x (- x)))
       (/
        (-
         (+ (/ -1.061405429 (pow t_0 4.0)) (/ -1.421413741 (pow t_0 2.0)))
         (+
          0.254829592
          (+ (/ -0.284496736 t_0) (/ -1.453152027 (pow t_0 3.0)))))
        t_0))))))
double code(double x) {
	return 1.0 - (((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (0.254829592 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-0.284496736 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (1.421413741 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * (-1.453152027 + ((1.0 / (1.0 + (0.3275911 * fabs(x)))) * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x))));
}
↓
double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	double tmp;
	if (fabs(x) <= 1e-8) {
		tmp = fma(pow(x, 3.0), 1.436724444676459, 1e-27) / (((x * x) * 1.2732557730789702) + (1e-18 - sqrt(pow((x * 1.128386358070218e-9), 2.0))));
	} else {
		tmp = 1.0 + (exp((x * -x)) * ((((-1.061405429 / pow(t_0, 4.0)) + (-1.421413741 / pow(t_0, 2.0))) - (0.254829592 + ((-0.284496736 / t_0) + (-1.453152027 / pow(t_0, 3.0))))) / t_0));
	}
	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)
	tmp = 0.0
	if (abs(x) <= 1e-8)
		tmp = Float64(fma((x ^ 3.0), 1.436724444676459, 1e-27) / Float64(Float64(Float64(x * x) * 1.2732557730789702) + Float64(1e-18 - sqrt((Float64(x * 1.128386358070218e-9) ^ 2.0)))));
	else
		tmp = Float64(1.0 + Float64(exp(Float64(x * Float64(-x))) * Float64(Float64(Float64(Float64(-1.061405429 / (t_0 ^ 4.0)) + Float64(-1.421413741 / (t_0 ^ 2.0))) - Float64(0.254829592 + Float64(Float64(-0.284496736 / t_0) + Float64(-1.453152027 / (t_0 ^ 3.0))))) / t_0)));
	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]}, If[LessEqual[N[Abs[x], $MachinePrecision], 1e-8], N[(N[(N[Power[x, 3.0], $MachinePrecision] * 1.436724444676459 + 1e-27), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * 1.2732557730789702), $MachinePrecision] + N[(1e-18 - N[Sqrt[N[Power[N[(x * 1.128386358070218e-9), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[Exp[N[(x * (-x)), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(-1.061405429 / N[Power[t$95$0, 4.0], $MachinePrecision]), $MachinePrecision] + N[(-1.421413741 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.254829592 + N[(N[(-0.284496736 / t$95$0), $MachinePrecision] + N[(-1.453152027 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $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)\\
\mathbf{if}\;\left|x\right| \leq 10^{-8}:\\
\;\;\;\;\frac{\mathsf{fma}\left({x}^{3}, 1.436724444676459, 10^{-27}\right)}{\left(x \cdot x\right) \cdot 1.2732557730789702 + \left(10^{-18} - \sqrt{{\left(x \cdot 1.128386358070218 \cdot 10^{-9}\right)}^{2}}\right)}\\

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


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if (fabs.f64 x) < 1e-8

    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. Simplified27.1

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

    3. Taylor expanded in x around 0 28.6

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

    4. Simplified29.5

      \[\leadsto \color{blue}{1 + \left(\left(\frac{1.453152027}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{4}} + \frac{0.284496736}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{2}}\right) - \left(\frac{0.254829592}{\mathsf{fma}\left(0.3275911, x, 1\right)} + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{5}} + \frac{1.421413741}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{3}}\right)\right)\right)} \]
      Proof
      (+.f64 1 (-.f64 (+.f64 (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1453152027/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 x 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 133 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 133 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 1) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 4)) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite<= metadata-eval (+.f64 3 1)))) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (/.f64 (*.f64 1453152027/1000000000 1) (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (/.f64 8890523/31250000 (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (Rewrite<= metadata-eval (*.f64 8890523/31250000 1)) (pow.f64 (fma.f64 3275911/10000000 x 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 133 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 133 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 1) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (/.f64 (*.f64 8890523/31250000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (Rewrite<= associate-*r/_binary64 (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (/.f64 31853699/125000000 (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 31853699/125000000 1)) (fma.f64 3275911/10000000 x 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (fma.f64 3275911/10000000 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (fma.f64 3275911/10000000 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 133 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (fma.f64 3275911/10000000 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (fma.f64 3275911/10000000 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 133 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (fma.f64 3275911/10000000 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 1)) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (/.f64 (*.f64 31853699/125000000 1) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1061405429/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 x 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 133 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 133 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 1) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 5)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite<= metadata-eval (+.f64 4 1)))) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (*.f64 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))))) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (Rewrite<= metadata-eval (*.f64 1421413741/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 x 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 1) 3)))))): 133 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 1) 3)))))): 0 points increase in error, 133 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 1) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 1 (-.f64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (Rewrite<= associate-*r/_binary64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3)))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 1 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 31853699/125000000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))))))): 1 points increase in error, 116 points decrease in error

    5. Taylor expanded in x around 0 0.9

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

    6. Applied egg-rr1.8

      \[\leadsto \color{blue}{\left(10^{-27} + {x}^{3} \cdot 1.436724444676459\right) \cdot \frac{1}{10^{-18} + \left({\left(1.128386358070218 \cdot x\right)}^{2} - 1.128386358070218 \cdot 10^{-9} \cdot x\right)}} \]

    7. Simplified0.9

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left({x}^{3}, 1.436724444676459, 10^{-27}\right)}{\left(x \cdot x\right) \cdot 1.2732557730789702 - \left(x \cdot 1.128386358070218 \cdot 10^{-9} - 10^{-18}\right)}} \]
      Proof
      (/.f64 (fma.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000 1/1000000000000000000000000000) (-.f64 (*.f64 (*.f64 x x) 318313943269742557644254641881/250000000000000000000000000000) (-.f64 (*.f64 x 564193179035109/500000000000000000000000) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000) 1/1000000000000000000000000000)) (-.f64 (*.f64 (*.f64 x x) 318313943269742557644254641881/250000000000000000000000000000) (-.f64 (*.f64 x 564193179035109/500000000000000000000000) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000))) (-.f64 (*.f64 (*.f64 x x) 318313943269742557644254641881/250000000000000000000000000000) (-.f64 (*.f64 x 564193179035109/500000000000000000000000) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (-.f64 (*.f64 (*.f64 x x) (Rewrite<= metadata-eval (*.f64 564193179035109/500000000000000 564193179035109/500000000000000))) (-.f64 (*.f64 x 564193179035109/500000000000000000000000) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (-.f64 (*.f64 (Rewrite<= sqr-neg_binary64 (*.f64 (neg.f64 x) (neg.f64 x))) (*.f64 564193179035109/500000000000000 564193179035109/500000000000000)) (-.f64 (*.f64 x 564193179035109/500000000000000000000000) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (-.f64 (*.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 564193179035109/500000000000000 564193179035109/500000000000000)) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 564193179035109/500000000000000000000000 x)) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (Rewrite=> fma-neg_binary64 (fma.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 564193179035109/500000000000000 564193179035109/500000000000000) (neg.f64 (-.f64 (*.f64 564193179035109/500000000000000000000000 x) 1/1000000000000000000))))): 2 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (fma.f64 (Rewrite=> sqr-neg_binary64 (*.f64 x x)) (*.f64 564193179035109/500000000000000 564193179035109/500000000000000) (neg.f64 (-.f64 (*.f64 564193179035109/500000000000000000000000 x) 1/1000000000000000000)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (*.f64 x x) (*.f64 564193179035109/500000000000000 564193179035109/500000000000000)) (-.f64 (*.f64 564193179035109/500000000000000000000000 x) 1/1000000000000000000)))): 0 points increase in error, 2 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (-.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 564193179035109/500000000000000 564193179035109/500000000000000) (*.f64 x x))) (-.f64 (*.f64 564193179035109/500000000000000000000000 x) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (-.f64 (Rewrite<= swap-sqr_binary64 (*.f64 (*.f64 564193179035109/500000000000000 x) (*.f64 564193179035109/500000000000000 x))) (-.f64 (*.f64 564193179035109/500000000000000000000000 x) 1/1000000000000000000))): 4 points increase in error, 25 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (-.f64 (Rewrite<= unpow2_binary64 (pow.f64 (*.f64 564193179035109/500000000000000 x) 2)) (-.f64 (*.f64 564193179035109/500000000000000000000000 x) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (pow.f64 (*.f64 564193179035109/500000000000000 x) 2) (*.f64 564193179035109/500000000000000000000000 x)) 1/1000000000000000000))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (Rewrite<= +-commutative_binary64 (+.f64 1/1000000000000000000 (-.f64 (pow.f64 (*.f64 564193179035109/500000000000000 x) 2) (*.f64 564193179035109/500000000000000000000000 x))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (Rewrite<= /-rgt-identity_binary64 (/.f64 (+.f64 1/1000000000000000000 (-.f64 (pow.f64 (*.f64 564193179035109/500000000000000 x) 2) (*.f64 564193179035109/500000000000000000000000 x))) 1))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) 1) (+.f64 1/1000000000000000000 (-.f64 (pow.f64 (*.f64 564193179035109/500000000000000 x) 2) (*.f64 564193179035109/500000000000000000000000 x))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 (+.f64 1/1000000000000000000000000000 (*.f64 (pow.f64 x 3) 179590555584557392343160168944680065920800029/125000000000000000000000000000000000000000000)) (/.f64 1 (+.f64 1/1000000000000000000 (-.f64 (pow.f64 (*.f64 564193179035109/500000000000000 x) 2) (*.f64 564193179035109/500000000000000000000000 x)))))): 117 points increase in error, 5 points decrease in error

    8. Applied egg-rr0.4

      \[\leadsto \frac{\mathsf{fma}\left({x}^{3}, 1.436724444676459, 10^{-27}\right)}{\left(x \cdot x\right) \cdot 1.2732557730789702 - \left(\color{blue}{\sqrt{{\left(x \cdot 1.128386358070218 \cdot 10^{-9}\right)}^{2}}} - 10^{-18}\right)} \]

    if 1e-8 < (fabs.f64 x)

    1. Initial program 0.4

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

    2. Simplified0.4

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

    3. Taylor expanded in x around inf 0.4

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

    4. Simplified0.4

      \[\leadsto \color{blue}{1 - \frac{\left(\frac{1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \frac{1.421413741}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}}\right) + \left(0.254829592 - \left(\frac{0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + \frac{1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}}\right)\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} \cdot e^{x \cdot \left(-x\right)}} \]
      Proof
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 4)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1061405429/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 4)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 4)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4)) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (/.f64 (Rewrite<= metadata-eval (*.f64 1421413741/1000000000 1)) (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (/.f64 (*.f64 1421413741/1000000000 1) (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (Rewrite<= associate-*r/_binary64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (-.f64 31853699/125000000 (+.f64 (/.f64 8890523/31250000 (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 8890523/31250000 1)) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 8890523/31250000 1) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 8890523/31250000 1) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 1453152027/1000000000 (pow.f64 (fma.f64 3275911/10000000 (fabs.f64 x) 1) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 1453152027/1000000000 (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 1453152027/1000000000 (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (/.f64 (Rewrite<= metadata-eval (*.f64 1453152027/1000000000 1)) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (-.f64 31853699/125000000 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) 31853699/125000000) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 117 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (Rewrite<= associate--l-_binary64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite<= metadata-eval (+.f64 2 1)))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (*.f64 (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (fma.f64 3275911/10000000 (fabs.f64 x) 1)) (exp.f64 (*.f64 x (neg.f64 x))))): 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 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (exp.f64 (*.f64 x (neg.f64 x))))): 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 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (exp.f64 (*.f64 x (neg.f64 x))))): 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 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x x)))))): 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 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (exp.f64 (neg.f64 (Rewrite<= unpow2_binary64 (pow.f64 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 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (pow.f64 x 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite=> associate--r+_binary64 (-.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (pow.f64 x 2)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 31853699/125000000 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4)))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (pow.f64 x 2)))))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (+.f64 (+.f64 31853699/125000000 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 4)))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (pow.f64 x 2)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (/.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (exp.f64 (neg.f64 (pow.f64 x 2)))))): 1 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 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (Rewrite<= +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (*.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 (pow.f64 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 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (Rewrite=> pow-plus_binary64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (+.f64 2 1)))))) (*.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 (pow.f64 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 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (Rewrite=> metadata-eval 3))))) (*.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 (pow.f64 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 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.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 (pow.f64 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 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))) (exp.f64 (neg.f64 (pow.f64 x 2)))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2))))) (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 2))))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3)))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.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))) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 1453152027/1000000000 1) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 3)))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.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 (*.f64 1453152027/1000000000 1) (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 3))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.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))) (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3))))))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 x 2))) (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (*.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 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))): 0 points increase in error, 0 points decrease in error
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 10^{-8}:\\ \;\;\;\;\frac{\mathsf{fma}\left({x}^{3}, 1.436724444676459, 10^{-27}\right)}{\left(x \cdot x\right) \cdot 1.2732557730789702 + \left(10^{-18} - \sqrt{{\left(x \cdot 1.128386358070218 \cdot 10^{-9}\right)}^{2}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + e^{x \cdot \left(-x\right)} \cdot \frac{\left(\frac{-1.061405429}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{4}} + \frac{-1.421413741}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{2}}\right) - \left(0.254829592 + \left(\frac{-0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + \frac{-1.453152027}{{\left(\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\right)}^{3}}\right)\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error0.4
Cost48388
\[\begin{array}{l} t_0 := 1 + \left|x\right| \cdot 0.3275911\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;\left|x\right| \leq 10^{-8}:\\ \;\;\;\;\frac{\mathsf{fma}\left({x}^{3}, 1.436724444676459, 10^{-27}\right)}{\left(x \cdot x\right) \cdot 1.2732557730789702 + \left(10^{-18} - \sqrt{{\left(x \cdot 1.128386358070218 \cdot 10^{-9}\right)}^{2}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 + t_1 \cdot \left(-1.421413741 + t_1 \cdot \left(1.453152027 + \frac{-1.061405429}{t_0}\right)\right)\right)\right)\right)\\ \end{array} \]
Alternative 2
Error0.5
Cost28292
\[\begin{array}{l} t_0 := \frac{1}{1 + \left|x\right| \cdot 0.3275911}\\ \mathbf{if}\;x \leq -0.3:\\ \;\;\;\;1 + t_0 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_0 \cdot \left(0.284496736 + t_0 \cdot \left(-1.029667143 + x \cdot -0.1283326989600778\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 3
Error0.5
Cost27908
\[\begin{array}{l} t_0 := 1 + \left|x\right| \cdot 0.3275911\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -0.5:\\ \;\;\;\;1 + t_1 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + \frac{0.284496736 + t_1 \cdot -1.029667143}{t_0}\right)\right)\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 4
Error0.5
Cost26308
\[\begin{array}{l} \mathbf{if}\;x \leq -0.72:\\ \;\;\;\;\mathsf{fma}\left(\frac{{\left(e^{-x}\right)}^{x}}{\mathsf{fma}\left(0.3275911, x, 1\right)}, -0.254829592, 1\right)\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 5
Error0.5
Cost22788
\[\begin{array}{l} t_0 := 1 + \left|x\right| \cdot 0.3275911\\ t_1 := 1 + x \cdot 0.3275911\\ t_2 := \frac{1}{t_1}\\ \mathbf{if}\;x \leq -0.72:\\ \;\;\;\;1 + t_2 \cdot \left(e^{x \cdot \left(-x\right)} \cdot \left(-0.254829592 + t_2 \cdot \left(0.284496736 + \frac{1}{t_0} \cdot \left(-1.421413741 + \left(-1.453152027 + \frac{1.061405429}{t_0}\right) \cdot \frac{-1}{t_1}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 6
Error0.5
Cost20100
\[\begin{array}{l} \mathbf{if}\;x \leq -0.78:\\ \;\;\;\;1 + -0.254829592 \cdot \frac{e^{x \cdot \left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 7
Error0.5
Cost13448
\[\begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 8
Error1.0
Cost6856
\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;\mathsf{fma}\left(1.128386358070218, x, 10^{-9}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 9
Error1.0
Cost584
\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.88:\\ \;\;\;\;10^{-9} + x \cdot 1.128386358070218\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 10
Error1.6
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 11
Error29.4
Cost64
\[10^{-9} \]

Error

Reproduce

herbie shell --seed 2022337 
(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)))))))