Average Error: 13.4 → 0.2
Time: 17.6s
Precision: binary64
Cost: 104900
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
↓
\[\begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ \mathbf{if}\;\left|x\right| \leq 2 \cdot 10^{-7}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\frac{-1.061405429}{{t_0}^{4}} + \left(\frac{1.453152027}{{t_0}^{3}} + \left(\frac{-1.421413741}{{t_0}^{2}} + \frac{0.284496736}{t_0}\right)\right)\right)}{t_0 \cdot {\left(e^{x}\right)}^{x}}\\ \end{array} \]
(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 (fabs x) 0.3275911 1.0)))
   (if (<= (fabs x) 2e-7)
     (+ 1e-9 (sqrt (pow (* x 1.128386358070218) 2.0)))
     (+
      1.0
      (/
       (+
        -0.254829592
        (+
         (/ -1.061405429 (pow t_0 4.0))
         (+
          (/ 1.453152027 (pow t_0 3.0))
          (+ (/ -1.421413741 (pow t_0 2.0)) (/ 0.284496736 t_0)))))
       (* t_0 (pow (exp x) x)))))))
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(fabs(x), 0.3275911, 1.0);
	double tmp;
	if (fabs(x) <= 2e-7) {
		tmp = 1e-9 + sqrt(pow((x * 1.128386358070218), 2.0));
	} else {
		tmp = 1.0 + ((-0.254829592 + ((-1.061405429 / pow(t_0, 4.0)) + ((1.453152027 / pow(t_0, 3.0)) + ((-1.421413741 / pow(t_0, 2.0)) + (0.284496736 / t_0))))) / (t_0 * pow(exp(x), x)));
	}
	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(abs(x), 0.3275911, 1.0)
	tmp = 0.0
	if (abs(x) <= 2e-7)
		tmp = Float64(1e-9 + sqrt((Float64(x * 1.128386358070218) ^ 2.0)));
	else
		tmp = Float64(1.0 + Float64(Float64(-0.254829592 + Float64(Float64(-1.061405429 / (t_0 ^ 4.0)) + Float64(Float64(1.453152027 / (t_0 ^ 3.0)) + Float64(Float64(-1.421413741 / (t_0 ^ 2.0)) + Float64(0.284496736 / t_0))))) / Float64(t_0 * (exp(x) ^ x))));
	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[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, If[LessEqual[N[Abs[x], $MachinePrecision], 2e-7], N[(1e-9 + N[Sqrt[N[Power[N[(x * 1.128386358070218), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(-0.254829592 + N[(N[(-1.061405429 / N[Power[t$95$0, 4.0], $MachinePrecision]), $MachinePrecision] + N[(N[(1.453152027 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-1.421413741 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] + N[(0.284496736 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 * N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]), $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(\left|x\right|, 0.3275911, 1\right)\\
\mathbf{if}\;\left|x\right| \leq 2 \cdot 10^{-7}:\\
\;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\

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


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if (fabs.f64 x) < 1.9999999999999999e-7

    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. Applied egg-rr27.3

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

    3. Taylor expanded in x around 0 1.0

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

    4. Applied egg-rr0.1

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

    if 1.9999999999999999e-7 < (fabs.f64 x)

    1. Initial program 0.2

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

    2. Taylor expanded in x around 0 0.3

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

    3. Simplified0.2

      \[\leadsto \color{blue}{1 - \frac{0.254829592 + \left(\frac{1.061405429}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{4}} + \left(\frac{-1.453152027}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{3}} + \left(\frac{1.421413741}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{2}} + \frac{-0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)\right)\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot {\left(e^{x}\right)}^{x}}} \]
      Proof
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 1061405429/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 4)) (+.f64 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1061405429/1000000000 1)) (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 4)) (+.f64 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) 3275911/10000000) 1)) 4)) (+.f64 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 3275911/10000000 (fabs.f64 x))) 1) 4)) (+.f64 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (/.f64 (*.f64 1061405429/1000000000 1) (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 4)) (+.f64 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 4)))) (+.f64 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (/.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 (/.f64 -1453152027/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (/.f64 (Rewrite<= metadata-eval (neg.f64 1453152027/1000000000)) (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (/.f64 (neg.f64 1453152027/1000000000) (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) 3275911/10000000) 1)) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (/.f64 (neg.f64 1453152027/1000000000) (pow.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 3275911/10000000 (fabs.f64 x))) 1) 3)) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (/.f64 (neg.f64 1453152027/1000000000) (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2)) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 3 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 (neg.f64 1453152027/1000000000) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2)))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (/.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1453152027/1000000000 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (Rewrite=> distribute-frac-neg_binary64 (neg.f64 (/.f64 (/.f64 1453152027/1000000000 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (Rewrite<= associate-/r*_binary64 (/.f64 1453152027/1000000000 (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2)) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2)))))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1453152027/1000000000 1)) (*.f64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2)) (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 3 2))))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (/.f64 (*.f64 1453152027/1000000000 1) (Rewrite<= sqr-pow_binary64 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 1 points increase in error, 3 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3))))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) 3275911/10000000) 1)) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 3275911/10000000 (fabs.f64 x))) 1) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (/.f64 1421413741/1000000000 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 1421413741/1000000000 1)) (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)))) (/.f64 -8890523/31250000 (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (/.f64 (Rewrite<= metadata-eval (neg.f64 8890523/31250000)) (fma.f64 (fabs.f64 x) 3275911/10000000 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (/.f64 (neg.f64 8890523/31250000) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) 3275911/10000000) 1))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (/.f64 (neg.f64 8890523/31250000) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 3275911/10000000 (fabs.f64 x))) 1)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 8890523/31250000 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 8890523/31250000 1)) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (neg.f64 (/.f64 (*.f64 8890523/31250000 1) (Rewrite=> +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (+.f64 (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))) (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (neg.f64 (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (Rewrite=> unsub-neg_binary64 (-.f64 (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (Rewrite<= associate--r+_binary64 (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (-.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 4))) (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 1421413741/1000000000 (/.f64 1 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2))) (neg.f64 (+.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))))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.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)))) (neg.f64 (+.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)))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 2 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (+.f64 31853699/125000000 (Rewrite<= sub-neg_binary64 (-.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 (*.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))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= associate--l+_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 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)))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 120 points increase in error, 3 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (Rewrite=> +-commutative_binary64 (+.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 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))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) 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 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)) 2)))) 31853699/125000000) (+.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))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.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 (*.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))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (-.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))))))) (*.f64 (fma.f64 (fabs.f64 x) 3275911/10000000 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (-.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)))))) (*.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) 3275911/10000000) 1)) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (-.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)))))) (*.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 3275911/10000000 (fabs.f64 x))) 1) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (-.f64 (+.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)))))) (*.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 1)) (pow.f64 (exp.f64 x) x)))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (-.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)))))) (*.f64 (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 1) (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (-.f64 (+.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)))))) (*.f64 (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 1) (exp.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 1 (-.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)))))) (*.f64 (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 1) (exp.f64 (Rewrite<= unpow2_binary64 (pow.f64 (fabs.f64 x) 2)))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (Rewrite=> *-lft-identity_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 (*.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)))))) (*.f64 (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 1) (exp.f64 (pow.f64 (fabs.f64 x) 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (-.f64 (+.f64 31853699/125000000 (+.f64 (*.f64 1061405429/1000000000 (/.f64 1 (pow.f64 (+.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<= associate-/r/_binary64 (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (/.f64 1 (exp.f64 (pow.f64 (fabs.f64 x) 2))))))): 1 points increase in error, 0 points decrease in error
      (-.f64 1 (/.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 (*.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))))) (/.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) (Rewrite<= exp-neg_binary64 (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2))))))): 0 points increase in error, 1 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 (*.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))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))): 1 points increase in error, 2 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (Rewrite=> associate--l+_binary64 (+.f64 31853699/125000000 (-.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 (*.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))))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 3 points increase in error, 120 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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 (Rewrite=> +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 2)))) (+.f64 (*.f64 8890523/31250000 (/.f64 1 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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 (*.f64 8890523/31250000 (/.f64 1 (Rewrite=> +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1) 3)))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (pow.f64 (Rewrite=> +-commutative_binary64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) 3)))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x)))))))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 1 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2)) (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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 (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))) (*.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)))))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (+.f64 31853699/125000000 (-.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)))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 1453152027/1000000000 (/.f64 1 (*.f64 (pow.f64 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))) 2) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1)))) (*.f64 8890523/31250000 (/.f64 1 (+.f64 1 (*.f64 3275911/10000000 (fabs.f64 x))))))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (Rewrite<= associate--l+_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)))))))) (exp.f64 (neg.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 (*.f64 3275911/10000000 (fabs.f64 x)) 1))): 120 points increase in error, 3 points decrease in error
      (-.f64 1 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.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 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 3275911/10000000 (fabs.f64 x)) 1))): 0 points increase in error, 0 points decrease in error
      (-.f64 1 (/.f64 (*.f64 (exp.f64 (neg.f64 (pow.f64 (fabs.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 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)))))): 0 points increase in error, 0 points decrease in error
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 2 \cdot 10^{-7}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\frac{-1.061405429}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{4}} + \left(\frac{1.453152027}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{3}} + \left(\frac{-1.421413741}{{\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{2}} + \frac{0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)\right)\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot {\left(e^{x}\right)}^{x}}\\ \end{array} \]

Alternatives

Alternative 1
Error0.5
Cost73032
\[\begin{array}{l} t_0 := 1 + \left|x\right| \cdot 0.3275911\\ t_1 := {\left(e^{x}\right)}^{x}\\ \mathbf{if}\;x \leq -0.1042389592740314:\\ \;\;\;\;1 + \frac{\frac{-0.254829592 + \frac{\left(0.284496736 + 1.453152027 \cdot \frac{1}{{t_0}^{2}}\right) + \left(\frac{1}{{t_0}^{3}} \cdot -1.061405429 + 1.421413741 \cdot \frac{-1}{t_0}\right)}{t_0}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{t_1}\\ \mathbf{elif}\;x \leq 2.8577931967385142 \cdot 10^{-18}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\frac{-1.421413741}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{2}} + \left(\frac{-1.061405429}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{4}} + \left(\frac{1.453152027}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{3}} + \frac{0.284496736}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)\right)\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot t_1}\\ \end{array} \]
Alternative 2
Error0.5
Cost67332
\[\begin{array}{l} t_0 := 1 + \left|x\right| \cdot 0.3275911\\ t_1 := {\left(e^{x}\right)}^{x}\\ \mathbf{if}\;x \leq -0.1042389592740314:\\ \;\;\;\;1 + \frac{\frac{-0.254829592 + \frac{\left(0.284496736 + 1.453152027 \cdot \frac{1}{{t_0}^{2}}\right) + \left(\frac{1}{{t_0}^{3}} \cdot -1.061405429 + 1.421413741 \cdot \frac{-1}{t_0}\right)}{t_0}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{t_1}\\ \mathbf{elif}\;x \leq 2.8577931967385142 \cdot 10^{-18}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\frac{-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{2}} + \frac{0.284496736}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{t_1 \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 3
Error1.1
Cost53704
\[\begin{array}{l} \mathbf{if}\;x \leq -6949695841.479063:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8577931967385142 \cdot 10^{-18}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\frac{-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{2}} + \frac{0.284496736}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 4
Error0.5
Cost53704
\[\begin{array}{l} t_0 := 1 + \left|x\right| \cdot 0.3275911\\ t_1 := \frac{1}{t_0}\\ \mathbf{if}\;x \leq -0.1042389592740314:\\ \;\;\;\;1 + e^{x \cdot \left(-x\right)} \cdot \left(t_1 \cdot \left(-0.254829592 + t_1 \cdot \left(0.284496736 + t_1 \cdot \left(-1.421413741 + t_1 \cdot \left(1.453152027 + 1.061405429 \cdot \frac{-1}{t_0}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.8577931967385142 \cdot 10^{-18}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \left(\frac{-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{{\left(\mathsf{fma}\left(0.3275911, x, 1\right)\right)}^{2}} + \frac{0.284496736}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 5
Error1.1
Cost47368
\[\begin{array}{l} \mathbf{if}\;x \leq -6949695841.479063:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8577931967385142 \cdot 10^{-18}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \frac{1}{\mathsf{fma}\left(0.3275911, x, 1\right)} \cdot \left(0.284496736 + \frac{-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}\right)}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 6
Error1.1
Cost47240
\[\begin{array}{l} \mathbf{if}\;x \leq -6949695841.479063:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8577931967385142 \cdot 10^{-18}:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-0.254829592 + \frac{0.284496736 + \frac{-1.421413741 + \frac{1.453152027 + \frac{-1.061405429}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{\mathsf{fma}\left(0.3275911, x, 1\right)}}{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left(0.3275911, x, 1\right)}\\ \end{array} \]
Alternative 7
Error0.5
Cost19716
\[\begin{array}{l} \mathbf{if}\;\left|x\right| \leq 0.2:\\ \;\;\;\;10^{-9} + \sqrt{{\left(x \cdot 1.128386358070218\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 8
Error1.0
Cost13384
\[\begin{array}{l} \mathbf{if}\;x \leq -1.3632784500000664 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.030677761684903028:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(x, -0.00011824294398844343, 1.128386358070218\right), 10^{-9}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 9
Error1.0
Cost7304
\[\begin{array}{l} \mathbf{if}\;x \leq -1.3632784500000664 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.030677761684903028:\\ \;\;\;\;10^{-9} + \left(x \cdot 1.128386358070218 + -0.00011824294398844343 \cdot {x}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 10
Error1.0
Cost584
\[\begin{array}{l} \mathbf{if}\;x \leq -1.3632784500000664 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.030677761684903028:\\ \;\;\;\;10^{-9} + x \cdot 1.128386358070218\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 11
Error27.0
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -0.1042389592740314:\\ \;\;\;\;0.745170408\\ \mathbf{elif}\;x \leq 2.691900019007884 \cdot 10^{-6}:\\ \;\;\;\;10^{-9}\\ \mathbf{else}:\\ \;\;\;\;0.745170408\\ \end{array} \]
Alternative 12
Error1.6
Cost328
\[\begin{array}{l} \mathbf{if}\;x \leq -0.1042389592740314:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.691900019007884 \cdot 10^{-6}:\\ \;\;\;\;10^{-9}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 13
Error30.0
Cost64
\[10^{-9} \]

Error

Reproduce

herbie shell --seed 2022295 
(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)))))))