Jmat.Real.erf

Percentage Accurate: 79.1% → 86.5%

Time: 18.9s

Alternatives: 16

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\\ 1 - \left(t\_0 \cdot \left(0.254829592 + t\_0 \cdot \left(-0.284496736 + t\_0 \cdot \left(1.421413741 + t\_0 \cdot \left(-1.453152027 + t\_0 \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))
   (-
    1.0
    (*
     (*
      t_0
      (+
       0.254829592
       (*
        t_0
        (+
         -0.284496736
         (*
          t_0
          (+ 1.421413741 (* t_0 (+ -1.453152027 (* t_0 1.061405429)))))))))
     (exp (- (* (fabs x) (fabs x))))))))

C

double code(double x) {
	double t_0 = 1.0 / (1.0 + (0.3275911 * fabs(x)));
	return 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = 1.0d0 / (1.0d0 + (0.3275911d0 * abs(x)))
    code = 1.0d0 - ((t_0 * (0.254829592d0 + (t_0 * ((-0.284496736d0) + (t_0 * (1.421413741d0 + (t_0 * ((-1.453152027d0) + (t_0 * 1.061405429d0))))))))) * exp(-(abs(x) * abs(x))))
end function

Java

public static double code(double x) {
	double t_0 = 1.0 / (1.0 + (0.3275911 * Math.abs(x)));
	return 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * Math.exp(-(Math.abs(x) * Math.abs(x))));
}

Python

def code(x):
	t_0 = 1.0 / (1.0 + (0.3275911 * math.fabs(x)))
	return 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * math.exp(-(math.fabs(x) * math.fabs(x))))

Julia

function code(x)
	t_0 = Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x))))
	return Float64(1.0 - Float64(Float64(t_0 * Float64(0.254829592 + Float64(t_0 * Float64(-0.284496736 + Float64(t_0 * Float64(1.421413741 + Float64(t_0 * Float64(-1.453152027 + Float64(t_0 * 1.061405429))))))))) * exp(Float64(-Float64(abs(x) * abs(x))))))
end

MATLAB

function tmp = code(x)
	t_0 = 1.0 / (1.0 + (0.3275911 * abs(x)));
	tmp = 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * exp(-(abs(x) * abs(x))));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(1.0 - N[(N[(t$95$0 * N[(0.254829592 + N[(t$95$0 * N[(-0.284496736 + N[(t$95$0 * N[(1.421413741 + N[(t$95$0 * N[(-1.453152027 + N[(t$95$0 * 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]]

Initial Program: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\\ 1 - \left(t\_0 \cdot \left(0.254829592 + t\_0 \cdot \left(-0.284496736 + t\_0 \cdot \left(1.421413741 + t\_0 \cdot \left(-1.453152027 + t\_0 \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))
   (-
    1.0
    (*
     (*
      t_0
      (+
       0.254829592
       (*
        t_0
        (+
         -0.284496736
         (*
          t_0
          (+ 1.421413741 (* t_0 (+ -1.453152027 (* t_0 1.061405429)))))))))
     (exp (- (* (fabs x) (fabs x))))))))

C

double code(double x) {
	double t_0 = 1.0 / (1.0 + (0.3275911 * fabs(x)));
	return 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * exp(-(fabs(x) * fabs(x))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = 1.0d0 / (1.0d0 + (0.3275911d0 * abs(x)))
    code = 1.0d0 - ((t_0 * (0.254829592d0 + (t_0 * ((-0.284496736d0) + (t_0 * (1.421413741d0 + (t_0 * ((-1.453152027d0) + (t_0 * 1.061405429d0))))))))) * exp(-(abs(x) * abs(x))))
end function

Java

public static double code(double x) {
	double t_0 = 1.0 / (1.0 + (0.3275911 * Math.abs(x)));
	return 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * Math.exp(-(Math.abs(x) * Math.abs(x))));
}

Python

def code(x):
	t_0 = 1.0 / (1.0 + (0.3275911 * math.fabs(x)))
	return 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * math.exp(-(math.fabs(x) * math.fabs(x))))

Julia

function code(x)
	t_0 = Float64(1.0 / Float64(1.0 + Float64(0.3275911 * abs(x))))
	return Float64(1.0 - Float64(Float64(t_0 * Float64(0.254829592 + Float64(t_0 * Float64(-0.284496736 + Float64(t_0 * Float64(1.421413741 + Float64(t_0 * Float64(-1.453152027 + Float64(t_0 * 1.061405429))))))))) * exp(Float64(-Float64(abs(x) * abs(x))))))
end

MATLAB

function tmp = code(x)
	t_0 = 1.0 / (1.0 + (0.3275911 * abs(x)));
	tmp = 1.0 - ((t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (t_0 * 1.061405429))))))))) * exp(-(abs(x) * abs(x))));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(1.0 / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(1.0 - N[(N[(t$95$0 * N[(0.254829592 + N[(t$95$0 * N[(-0.284496736 + N[(t$95$0 * N[(1.421413741 + N[(t$95$0 * N[(-1.453152027 + N[(t$95$0 * 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]]

Alternative 1: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)\\ t_2 := 0.254829592 + \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_0}}{t\_0}}{t\_1}}{t\_1}\\ t_3 := \frac{t\_2}{{\left(e^{x}\right)}^{x} \cdot t\_0}\\ t_4 := \mathsf{fma}\left(t\_3, \mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{t\_0}, t\_2, 1\right), 1\right)\\ t_5 := {t\_3}^{3}\\ \frac{{t\_4}^{-2} - {\left(\frac{-t\_5}{t\_4}\right)}^{2}}{\frac{t\_5}{t\_4} + {t\_4}^{-1}} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (fma -0.3275911 (fabs x) -1.0))
        (t_2
         (+
          0.254829592
          (/
           (+
            0.284496736
            (/
             (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_0)) t_0))
             t_1))
           t_1)))
        (t_3 (/ t_2 (* (pow (exp x) x) t_0)))
        (t_4 (fma t_3 (fma (/ (pow (exp x) (- x)) t_0) t_2 1.0) 1.0))
        (t_5 (pow t_3 3.0)))
   (/
    (- (pow t_4 -2.0) (pow (/ (- t_5) t_4) 2.0))
    (+ (/ t_5 t_4) (pow t_4 -1.0)))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma(-0.3275911, fabs(x), -1.0);
	double t_2 = 0.254829592 + ((0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / t_0)) / t_0)) / t_1)) / t_1);
	double t_3 = t_2 / (pow(exp(x), x) * t_0);
	double t_4 = fma(t_3, fma((pow(exp(x), -x) / t_0), t_2, 1.0), 1.0);
	double t_5 = pow(t_3, 3.0);
	return (pow(t_4, -2.0) - pow((-t_5 / t_4), 2.0)) / ((t_5 / t_4) + pow(t_4, -1.0));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(-0.3275911, abs(x), -1.0)
	t_2 = Float64(0.254829592 + Float64(Float64(0.284496736 + Float64(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_0)) / t_0)) / t_1)) / t_1))
	t_3 = Float64(t_2 / Float64((exp(x) ^ x) * t_0))
	t_4 = fma(t_3, fma(Float64((exp(x) ^ Float64(-x)) / t_0), t_2, 1.0), 1.0)
	t_5 = t_3 ^ 3.0
	return Float64(Float64((t_4 ^ -2.0) - (Float64(Float64(-t_5) / t_4) ^ 2.0)) / Float64(Float64(t_5 / t_4) + (t_4 ^ -1.0)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(0.254829592 + N[(N[(0.284496736 + N[(N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(N[(N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision] / t$95$0), $MachinePrecision] * t$95$2 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[Power[t$95$3, 3.0], $MachinePrecision]}, N[(N[(N[Power[t$95$4, -2.0], $MachinePrecision] - N[Power[N[((-t$95$5) / t$95$4), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$5 / t$95$4), $MachinePrecision] + N[Power[t$95$4, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 78.7%

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

4. Applied rewrites 79.5%

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

6. Applied rewrites 80.2%

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

   1. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   2. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   4. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   5. flip3-+ N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\color{blue}{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + {\frac{-1453152027}{1000000000}}^{3}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   6. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\color{blue}{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + {\frac{-1453152027}{1000000000}}^{3}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   7. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\color{blue}{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + {\frac{-1453152027}{1000000000}}^{3}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   8. lower-pow.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\color{blue}{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3}} + {\frac{-1453152027}{1000000000}}^{3}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + \color{blue}{\frac{-3068549660061560529467443683}{1000000000000000000000000000}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   10. associate-+r- N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + \frac{-3068549660061560529467443683}{1000000000000000000000000000}}{\color{blue}{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000}\right) - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   11. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + \frac{-3068549660061560529467443683}{1000000000000000000000000000}}{\color{blue}{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000}\right) - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

8. Applied rewrites 80.2%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\color{blue}{\frac{{\left(\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{3} + -3.0685496600615605}{\left({\left(\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{2} + 2.111650813574209\right) - \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot -1.453152027}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

10. Applied rewrites 86.2%

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

11. Final simplification 86.2%

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

Alternative 2: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)\\ t_1 := {\left(e^{x}\right)}^{\left(-x\right)}\\ t_2 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_3 := \frac{\frac{\frac{\frac{1.061405429}{t\_2} + -1.453152027}{t\_2} + 1.421413741}{t\_2} + -0.284496736}{t\_2} + 0.254829592\\ t_4 := {\left(e^{x}\right)}^{x}\\ t_5 := \mathsf{fma}\left(\frac{t\_3}{t\_4}, \frac{\mathsf{fma}\left(\frac{t\_1}{t\_2}, t\_3, 1\right)}{t\_2}, 1\right)\\ t_6 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_7 := 0.254829592 + \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_6}}{t\_6}}{t\_0}}{t\_0}\\ \mathsf{fma}\left(t\_5, {t\_5}^{-2}, \frac{-1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{t\_1}{t\_6}, t\_7, 1\right)}{t\_6}, \frac{t\_7}{t\_4}, 1\right)} \cdot {\left(\frac{\frac{\frac{\frac{\left(\frac{1.061405429}{{t\_6}^{2}} + 1.421413741\right) - \frac{1.453152027}{t\_6}}{t\_2} + -0.284496736}{t\_2} + 0.254829592}{t\_2}}{t\_4}\right)}^{3}\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma -0.3275911 (fabs x) -1.0))
        (t_1 (pow (exp x) (- x)))
        (t_2 (fma 0.3275911 (fabs x) 1.0))
        (t_3
         (+
          (/
           (+
            (/
             (+ (/ (+ (/ 1.061405429 t_2) -1.453152027) t_2) 1.421413741)
             t_2)
            -0.284496736)
           t_2)
          0.254829592))
        (t_4 (pow (exp x) x))
        (t_5 (fma (/ t_3 t_4) (/ (fma (/ t_1 t_2) t_3 1.0) t_2) 1.0))
        (t_6 (fma (fabs x) 0.3275911 1.0))
        (t_7
         (+
          0.254829592
          (/
           (+
            0.284496736
            (/
             (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_6)) t_6))
             t_0))
           t_0))))
   (fma
    t_5
    (pow t_5 -2.0)
    (*
     (/ -1.0 (fma (/ (fma (/ t_1 t_6) t_7 1.0) t_6) (/ t_7 t_4) 1.0))
     (pow
      (/
       (/
        (+
         (/
          (+
           (/
            (-
             (+ (/ 1.061405429 (pow t_6 2.0)) 1.421413741)
             (/ 1.453152027 t_6))
            t_2)
           -0.284496736)
          t_2)
         0.254829592)
        t_2)
       t_4)
      3.0)))))

C

double code(double x) {
	double t_0 = fma(-0.3275911, fabs(x), -1.0);
	double t_1 = pow(exp(x), -x);
	double t_2 = fma(0.3275911, fabs(x), 1.0);
	double t_3 = (((((((1.061405429 / t_2) + -1.453152027) / t_2) + 1.421413741) / t_2) + -0.284496736) / t_2) + 0.254829592;
	double t_4 = pow(exp(x), x);
	double t_5 = fma((t_3 / t_4), (fma((t_1 / t_2), t_3, 1.0) / t_2), 1.0);
	double t_6 = fma(fabs(x), 0.3275911, 1.0);
	double t_7 = 0.254829592 + ((0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / t_6)) / t_6)) / t_0)) / t_0);
	return fma(t_5, pow(t_5, -2.0), ((-1.0 / fma((fma((t_1 / t_6), t_7, 1.0) / t_6), (t_7 / t_4), 1.0)) * pow((((((((((1.061405429 / pow(t_6, 2.0)) + 1.421413741) - (1.453152027 / t_6)) / t_2) + -0.284496736) / t_2) + 0.254829592) / t_2) / t_4), 3.0)));
}

Julia

function code(x)
	t_0 = fma(-0.3275911, abs(x), -1.0)
	t_1 = exp(x) ^ Float64(-x)
	t_2 = fma(0.3275911, abs(x), 1.0)
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_2) + -1.453152027) / t_2) + 1.421413741) / t_2) + -0.284496736) / t_2) + 0.254829592)
	t_4 = exp(x) ^ x
	t_5 = fma(Float64(t_3 / t_4), Float64(fma(Float64(t_1 / t_2), t_3, 1.0) / t_2), 1.0)
	t_6 = fma(abs(x), 0.3275911, 1.0)
	t_7 = Float64(0.254829592 + Float64(Float64(0.284496736 + Float64(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_6)) / t_6)) / t_0)) / t_0))
	return fma(t_5, (t_5 ^ -2.0), Float64(Float64(-1.0 / fma(Float64(fma(Float64(t_1 / t_6), t_7, 1.0) / t_6), Float64(t_7 / t_4), 1.0)) * (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / (t_6 ^ 2.0)) + 1.421413741) - Float64(1.453152027 / t_6)) / t_2) + -0.284496736) / t_2) + 0.254829592) / t_2) / t_4) ^ 3.0)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision]}, Block[{t$95$2 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$2), $MachinePrecision] + -1.453152027), $MachinePrecision] / t$95$2), $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$2), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$2), $MachinePrecision] + 0.254829592), $MachinePrecision]}, Block[{t$95$4 = N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 / t$95$4), $MachinePrecision] * N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] * t$95$3 + 1.0), $MachinePrecision] / t$95$2), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(0.254829592 + N[(N[(0.284496736 + N[(N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$6), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, N[(t$95$5 * N[Power[t$95$5, -2.0], $MachinePrecision] + N[(N[(-1.0 / N[(N[(N[(N[(t$95$1 / t$95$6), $MachinePrecision] * t$95$7 + 1.0), $MachinePrecision] / t$95$6), $MachinePrecision] * N[(t$95$7 / t$95$4), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / N[Power[t$95$6, 2.0], $MachinePrecision]), $MachinePrecision] + 1.421413741), $MachinePrecision] - N[(1.453152027 / t$95$6), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$2), $MachinePrecision] + 0.254829592), $MachinePrecision] / t$95$2), $MachinePrecision] / t$95$4), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Initial program 78.7%

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

4. Applied rewrites 79.5%

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

6. Applied rewrites 80.2%

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

8. Applied rewrites 80.2%

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

9. Taylor expanded in x around 0

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\left(\frac{1421413741}{1000000000} + \frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]
10. Step-by-step derivation

    1. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\left(\frac{1421413741}{1000000000} + \frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    2. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\left(\frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}} + \frac{1421413741}{1000000000}\right)} - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    3. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\left(\frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}} + \frac{1421413741}{1000000000}\right)} - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    4. associate-*r/ N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\color{blue}{\frac{\frac{1061405429}{1000000000} \cdot 1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    5. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\color{blue}{\frac{1061405429}{1000000000}}}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    6. lower-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\color{blue}{\frac{\frac{1061405429}{1000000000}}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    7. lower-pow.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    8. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\color{blue}{\left(\frac{3275911}{10000000} \cdot \left|x\right| + 1\right)}}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    9. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    10. lower-fma.f64 N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\color{blue}{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    11. lower-fabs.f64 N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\color{blue}{\left|x\right|}, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    12. associate-*r/ N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \color{blue}{\frac{\frac{1453152027}{1000000000} \cdot 1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    13. metadata-eval N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\color{blue}{\frac{1453152027}{1000000000}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    14. lower-/.f64 N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \color{blue}{\frac{\frac{1453152027}{1000000000}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    15. +-commutative N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\frac{1453152027}{1000000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    16. *-commutative N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\frac{1453152027}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

    17. lower-fma.f64 N/A

        \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\frac{1453152027}{1000000000}}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

11. Applied rewrites 80.3%

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

12. Final simplification 80.3%

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

Alternative 3: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)\\ t_1 := {\left(e^{x}\right)}^{\left(-x\right)}\\ t_2 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_3 := \frac{\frac{\frac{\frac{1.061405429}{t\_2} + -1.453152027}{t\_2} + 1.421413741}{t\_2} + -0.284496736}{t\_2} + 0.254829592\\ t_4 := {\left(e^{x}\right)}^{x}\\ t_5 := \mathsf{fma}\left(\frac{t\_3}{t\_4}, \frac{\mathsf{fma}\left(\frac{t\_1}{t\_2}, t\_3, 1\right)}{t\_2}, 1\right)\\ t_6 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_7 := -1.453152027 + \frac{1.061405429}{t\_6}\\ t_8 := 0.254829592 + \frac{0.284496736 + \frac{1.421413741 + \frac{t\_7}{t\_6}}{t\_0}}{t\_0}\\ \mathsf{fma}\left(t\_5, {t\_5}^{-2}, \frac{-1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{t\_1}{t\_6}, t\_8, 1\right)}{t\_6}, \frac{t\_8}{t\_4}, 1\right)} \cdot {\left(\frac{\frac{\frac{\frac{\mathsf{fma}\left(t\_7, {t\_6}^{-1}, 1.421413741\right)}{t\_2} + -0.284496736}{t\_2} + 0.254829592}{t\_2}}{t\_4}\right)}^{3}\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma -0.3275911 (fabs x) -1.0))
        (t_1 (pow (exp x) (- x)))
        (t_2 (fma 0.3275911 (fabs x) 1.0))
        (t_3
         (+
          (/
           (+
            (/
             (+ (/ (+ (/ 1.061405429 t_2) -1.453152027) t_2) 1.421413741)
             t_2)
            -0.284496736)
           t_2)
          0.254829592))
        (t_4 (pow (exp x) x))
        (t_5 (fma (/ t_3 t_4) (/ (fma (/ t_1 t_2) t_3 1.0) t_2) 1.0))
        (t_6 (fma (fabs x) 0.3275911 1.0))
        (t_7 (+ -1.453152027 (/ 1.061405429 t_6)))
        (t_8
         (+
          0.254829592
          (/ (+ 0.284496736 (/ (+ 1.421413741 (/ t_7 t_6)) t_0)) t_0))))
   (fma
    t_5
    (pow t_5 -2.0)
    (*
     (/ -1.0 (fma (/ (fma (/ t_1 t_6) t_8 1.0) t_6) (/ t_8 t_4) 1.0))
     (pow
      (/
       (/
        (+
         (/ (+ (/ (fma t_7 (pow t_6 -1.0) 1.421413741) t_2) -0.284496736) t_2)
         0.254829592)
        t_2)
       t_4)
      3.0)))))

C

double code(double x) {
	double t_0 = fma(-0.3275911, fabs(x), -1.0);
	double t_1 = pow(exp(x), -x);
	double t_2 = fma(0.3275911, fabs(x), 1.0);
	double t_3 = (((((((1.061405429 / t_2) + -1.453152027) / t_2) + 1.421413741) / t_2) + -0.284496736) / t_2) + 0.254829592;
	double t_4 = pow(exp(x), x);
	double t_5 = fma((t_3 / t_4), (fma((t_1 / t_2), t_3, 1.0) / t_2), 1.0);
	double t_6 = fma(fabs(x), 0.3275911, 1.0);
	double t_7 = -1.453152027 + (1.061405429 / t_6);
	double t_8 = 0.254829592 + ((0.284496736 + ((1.421413741 + (t_7 / t_6)) / t_0)) / t_0);
	return fma(t_5, pow(t_5, -2.0), ((-1.0 / fma((fma((t_1 / t_6), t_8, 1.0) / t_6), (t_8 / t_4), 1.0)) * pow(((((((fma(t_7, pow(t_6, -1.0), 1.421413741) / t_2) + -0.284496736) / t_2) + 0.254829592) / t_2) / t_4), 3.0)));
}

Julia

function code(x)
	t_0 = fma(-0.3275911, abs(x), -1.0)
	t_1 = exp(x) ^ Float64(-x)
	t_2 = fma(0.3275911, abs(x), 1.0)
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_2) + -1.453152027) / t_2) + 1.421413741) / t_2) + -0.284496736) / t_2) + 0.254829592)
	t_4 = exp(x) ^ x
	t_5 = fma(Float64(t_3 / t_4), Float64(fma(Float64(t_1 / t_2), t_3, 1.0) / t_2), 1.0)
	t_6 = fma(abs(x), 0.3275911, 1.0)
	t_7 = Float64(-1.453152027 + Float64(1.061405429 / t_6))
	t_8 = Float64(0.254829592 + Float64(Float64(0.284496736 + Float64(Float64(1.421413741 + Float64(t_7 / t_6)) / t_0)) / t_0))
	return fma(t_5, (t_5 ^ -2.0), Float64(Float64(-1.0 / fma(Float64(fma(Float64(t_1 / t_6), t_8, 1.0) / t_6), Float64(t_8 / t_4), 1.0)) * (Float64(Float64(Float64(Float64(Float64(Float64(fma(t_7, (t_6 ^ -1.0), 1.421413741) / t_2) + -0.284496736) / t_2) + 0.254829592) / t_2) / t_4) ^ 3.0)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision]}, Block[{t$95$2 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$2), $MachinePrecision] + -1.453152027), $MachinePrecision] / t$95$2), $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$2), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$2), $MachinePrecision] + 0.254829592), $MachinePrecision]}, Block[{t$95$4 = N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 / t$95$4), $MachinePrecision] * N[(N[(N[(t$95$1 / t$95$2), $MachinePrecision] * t$95$3 + 1.0), $MachinePrecision] / t$95$2), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$6 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$7 = N[(-1.453152027 + N[(1.061405429 / t$95$6), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(0.254829592 + N[(N[(0.284496736 + N[(N[(1.421413741 + N[(t$95$7 / t$95$6), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, N[(t$95$5 * N[Power[t$95$5, -2.0], $MachinePrecision] + N[(N[(-1.0 / N[(N[(N[(N[(t$95$1 / t$95$6), $MachinePrecision] * t$95$8 + 1.0), $MachinePrecision] / t$95$6), $MachinePrecision] * N[(t$95$8 / t$95$4), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(N[(N[(N[(N[(t$95$7 * N[Power[t$95$6, -1.0], $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$2), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$2), $MachinePrecision] + 0.254829592), $MachinePrecision] / t$95$2), $MachinePrecision] / t$95$4), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Initial program 78.7%

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

4. Applied rewrites 79.5%

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

6. Applied rewrites 80.2%

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

8. Applied rewrites 80.2%

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

   1. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   2. lift-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   3. div-inv N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   4. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   6. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   7. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   8. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\color{blue}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   9. lift-fabs.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \color{blue}{\left|x\right|}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   10. lift-fabs.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \color{blue}{\left|x\right|}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   13. lift-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

   14. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\color{blue}{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}, \frac{1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{1421413741}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{1}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}, 1\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)} + \frac{31853699}{125000000}}{{\left(e^{x}\right)}^{x}}, 1\right)}\right) \]

10. Applied rewrites 80.2%

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

11. Final simplification 80.2%

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

Alternative 4: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)\\ t_2 := 0.254829592 + \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_0}}{t\_0}}{t\_1}}{t\_1}\\ t_3 := \frac{t\_2}{{\left(e^{x}\right)}^{x} \cdot t\_0}\\ t_4 := \mathsf{fma}\left(t\_3, \mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{t\_0}, t\_2, 1\right), 1\right)\\ \mathsf{fma}\left(t\_4, {t\_4}^{-2}, \frac{-{t\_3}^{3}}{t\_4}\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (fma -0.3275911 (fabs x) -1.0))
        (t_2
         (+
          0.254829592
          (/
           (+
            0.284496736
            (/
             (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_0)) t_0))
             t_1))
           t_1)))
        (t_3 (/ t_2 (* (pow (exp x) x) t_0)))
        (t_4 (fma t_3 (fma (/ (pow (exp x) (- x)) t_0) t_2 1.0) 1.0)))
   (fma t_4 (pow t_4 -2.0) (/ (- (pow t_3 3.0)) t_4))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma(-0.3275911, fabs(x), -1.0);
	double t_2 = 0.254829592 + ((0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / t_0)) / t_0)) / t_1)) / t_1);
	double t_3 = t_2 / (pow(exp(x), x) * t_0);
	double t_4 = fma(t_3, fma((pow(exp(x), -x) / t_0), t_2, 1.0), 1.0);
	return fma(t_4, pow(t_4, -2.0), (-pow(t_3, 3.0) / t_4));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(-0.3275911, abs(x), -1.0)
	t_2 = Float64(0.254829592 + Float64(Float64(0.284496736 + Float64(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_0)) / t_0)) / t_1)) / t_1))
	t_3 = Float64(t_2 / Float64((exp(x) ^ x) * t_0))
	t_4 = fma(t_3, fma(Float64((exp(x) ^ Float64(-x)) / t_0), t_2, 1.0), 1.0)
	return fma(t_4, (t_4 ^ -2.0), Float64(Float64(-(t_3 ^ 3.0)) / t_4))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(0.254829592 + N[(N[(0.284496736 + N[(N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(N[(N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision] / t$95$0), $MachinePrecision] * t$95$2 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]}, N[(t$95$4 * N[Power[t$95$4, -2.0], $MachinePrecision] + N[((-N[Power[t$95$3, 3.0], $MachinePrecision]) / t$95$4), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 78.7%

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

4. Applied rewrites 79.5%

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

6. Applied rewrites 80.2%

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

   1. lift-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   2. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   4. lift-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   5. flip3-+ N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\color{blue}{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + {\frac{-1453152027}{1000000000}}^{3}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   6. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\color{blue}{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + {\frac{-1453152027}{1000000000}}^{3}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   7. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\color{blue}{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + {\frac{-1453152027}{1000000000}}^{3}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   8. lower-pow.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\color{blue}{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3}} + {\frac{-1453152027}{1000000000}}^{3}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + \color{blue}{\frac{-3068549660061560529467443683}{1000000000000000000000000000}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \left(\frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   10. associate-+r- N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + \frac{-3068549660061560529467443683}{1000000000000000000000000000}}{\color{blue}{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000}\right) - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

   11. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}^{3} + \frac{-3068549660061560529467443683}{1000000000000000000000000000}}{\color{blue}{\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000} \cdot \frac{-1453152027}{1000000000}\right) - \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{-1453152027}{1000000000}}}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{\frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, \frac{31853699}{125000000} + \frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

8. Applied rewrites 80.2%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right), {\left(\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)\right)}^{-2}, -{\left(\frac{\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\color{blue}{\frac{{\left(\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{3} + -3.0685496600615605}{\left({\left(\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{2} + 2.111650813574209\right) - \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot -1.453152027}}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}\right)}^{3} \cdot \frac{\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{{\left(\mathsf{fma}\left(\frac{0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{{\left(e^{x}\right)}^{x}}, \frac{\mathsf{fma}\left(\frac{{\left(e^{x}\right)}^{\left(-x\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 0.254829592 + \frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)\right)}^{2}}\right) \]

10. Applied rewrites 80.2%

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

11. Final simplification 80.2%

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

Alternative 5: 80.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := 1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_0}}{t\_0}\\ t_2 := \frac{\frac{t\_1}{t\_0} + -0.284496736}{t\_0} + 0.254829592\\ t_3 := {\left(e^{x}\right)}^{x} \cdot t\_0\\ t_4 := \mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)\\ \frac{1 - \frac{1}{\frac{{t\_3}^{3}}{{\left(0.254829592 + \frac{0.284496736 + \frac{t\_1}{t\_4}}{t\_4}\right)}^{3}}}}{\mathsf{fma}\left(\frac{t\_2}{t\_3}, \mathsf{fma}\left({\left(e^{x}\right)}^{\left(-x\right)}, \frac{t\_2}{t\_0}, 1\right), 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_0)) t_0)))
        (t_2 (+ (/ (+ (/ t_1 t_0) -0.284496736) t_0) 0.254829592))
        (t_3 (* (pow (exp x) x) t_0))
        (t_4 (fma -0.3275911 (fabs x) -1.0)))
   (/
    (-
     1.0
     (/
      1.0
      (/
       (pow t_3 3.0)
       (pow (+ 0.254829592 (/ (+ 0.284496736 (/ t_1 t_4)) t_4)) 3.0))))
    (fma (/ t_2 t_3) (fma (pow (exp x) (- x)) (/ t_2 t_0) 1.0) 1.0))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = 1.421413741 + ((-1.453152027 + (1.061405429 / t_0)) / t_0);
	double t_2 = (((t_1 / t_0) + -0.284496736) / t_0) + 0.254829592;
	double t_3 = pow(exp(x), x) * t_0;
	double t_4 = fma(-0.3275911, fabs(x), -1.0);
	return (1.0 - (1.0 / (pow(t_3, 3.0) / pow((0.254829592 + ((0.284496736 + (t_1 / t_4)) / t_4)), 3.0)))) / fma((t_2 / t_3), fma(pow(exp(x), -x), (t_2 / t_0), 1.0), 1.0);
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_0)) / t_0))
	t_2 = Float64(Float64(Float64(Float64(t_1 / t_0) + -0.284496736) / t_0) + 0.254829592)
	t_3 = Float64((exp(x) ^ x) * t_0)
	t_4 = fma(-0.3275911, abs(x), -1.0)
	return Float64(Float64(1.0 - Float64(1.0 / Float64((t_3 ^ 3.0) / (Float64(0.254829592 + Float64(Float64(0.284496736 + Float64(t_1 / t_4)) / t_4)) ^ 3.0)))) / fma(Float64(t_2 / t_3), fma((exp(x) ^ Float64(-x)), Float64(t_2 / t_0), 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(t$95$1 / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision]}, Block[{t$95$3 = N[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]}, N[(N[(1.0 - N[(1.0 / N[(N[Power[t$95$3, 3.0], $MachinePrecision] / N[Power[N[(0.254829592 + N[(N[(0.284496736 + N[(t$95$1 / t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$2 / t$95$3), $MachinePrecision] * N[(N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision] * N[(t$95$2 / t$95$0), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 78.7%

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

4. Applied rewrites 78.8%

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

6. Applied rewrites 79.9%

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

7. Final simplification 79.9%

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

Alternative 6: 79.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(e^{x}\right)}^{\left(-x\right)}\\ t_1 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_2 := 1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_1}}{t\_1}\\ t_3 := \frac{\frac{t\_2}{t\_1} + -0.284496736}{t\_1} + 0.254829592\\ t_4 := \mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)\\ \frac{1 - \frac{{\left(t\_0 \cdot \left(0.254829592 + \frac{0.284496736 + \frac{t\_2}{t\_4}}{t\_4}\right)\right)}^{3}}{{t\_1}^{3}}}{\mathsf{fma}\left(\frac{t\_3}{{\left(e^{x}\right)}^{x} \cdot t\_1}, \mathsf{fma}\left(t\_0, \frac{t\_3}{t\_1}, 1\right), 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (pow (exp x) (- x)))
        (t_1 (fma (fabs x) 0.3275911 1.0))
        (t_2 (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_1)) t_1)))
        (t_3 (+ (/ (+ (/ t_2 t_1) -0.284496736) t_1) 0.254829592))
        (t_4 (fma -0.3275911 (fabs x) -1.0)))
   (/
    (-
     1.0
     (/
      (pow (* t_0 (+ 0.254829592 (/ (+ 0.284496736 (/ t_2 t_4)) t_4))) 3.0)
      (pow t_1 3.0)))
    (fma (/ t_3 (* (pow (exp x) x) t_1)) (fma t_0 (/ t_3 t_1) 1.0) 1.0))))

C

double code(double x) {
	double t_0 = pow(exp(x), -x);
	double t_1 = fma(fabs(x), 0.3275911, 1.0);
	double t_2 = 1.421413741 + ((-1.453152027 + (1.061405429 / t_1)) / t_1);
	double t_3 = (((t_2 / t_1) + -0.284496736) / t_1) + 0.254829592;
	double t_4 = fma(-0.3275911, fabs(x), -1.0);
	return (1.0 - (pow((t_0 * (0.254829592 + ((0.284496736 + (t_2 / t_4)) / t_4))), 3.0) / pow(t_1, 3.0))) / fma((t_3 / (pow(exp(x), x) * t_1)), fma(t_0, (t_3 / t_1), 1.0), 1.0);
}

Julia

function code(x)
	t_0 = exp(x) ^ Float64(-x)
	t_1 = fma(abs(x), 0.3275911, 1.0)
	t_2 = Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_1)) / t_1))
	t_3 = Float64(Float64(Float64(Float64(t_2 / t_1) + -0.284496736) / t_1) + 0.254829592)
	t_4 = fma(-0.3275911, abs(x), -1.0)
	return Float64(Float64(1.0 - Float64((Float64(t_0 * Float64(0.254829592 + Float64(Float64(0.284496736 + Float64(t_2 / t_4)) / t_4))) ^ 3.0) / (t_1 ^ 3.0))) / fma(Float64(t_3 / Float64((exp(x) ^ x) * t_1)), fma(t_0, Float64(t_3 / t_1), 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(t$95$2 / t$95$1), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$1), $MachinePrecision] + 0.254829592), $MachinePrecision]}, Block[{t$95$4 = N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]}, N[(N[(1.0 - N[(N[Power[N[(t$95$0 * N[(0.254829592 + N[(N[(0.284496736 + N[(t$95$2 / t$95$4), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision] / N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$3 / N[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(t$95$3 / t$95$1), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 78.7%

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

4. Applied rewrites 78.8%

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

6. Applied rewrites 78.8%

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

7. Final simplification 78.8%

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

Alternative 7: 79.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_0}}{t\_0}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)\\ t_2 := \frac{\frac{t\_1}{{\left(e^{x}\right)}^{x}}}{t\_0}\\ \frac{1 - {t\_2}^{3}}{\mathsf{fma}\left(\frac{t\_1}{t\_0}, {\left(e^{x}\right)}^{\left(-x\right)}, 1\right) \cdot t\_2 + 1} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1
         (fma
          (fma (fabs x) 0.3275911 -1.0)
          (/
           (+
            0.284496736
            (/
             (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_0)) t_0))
             (fma -0.3275911 (fabs x) -1.0)))
           (fma (* -0.10731592879921 x) x 1.0))
          0.254829592))
        (t_2 (/ (/ t_1 (pow (exp x) x)) t_0)))
   (/
    (- 1.0 (pow t_2 3.0))
    (+ (* (fma (/ t_1 t_0) (pow (exp x) (- x)) 1.0) t_2) 1.0))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma(fma(fabs(x), 0.3275911, -1.0), ((0.284496736 + ((1.421413741 + ((-1.453152027 + (1.061405429 / t_0)) / t_0)) / fma(-0.3275911, fabs(x), -1.0))) / fma((-0.10731592879921 * x), x, 1.0)), 0.254829592);
	double t_2 = (t_1 / pow(exp(x), x)) / t_0;
	return (1.0 - pow(t_2, 3.0)) / ((fma((t_1 / t_0), pow(exp(x), -x), 1.0) * t_2) + 1.0);
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(fma(abs(x), 0.3275911, -1.0), Float64(Float64(0.284496736 + Float64(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_0)) / t_0)) / fma(-0.3275911, abs(x), -1.0))) / fma(Float64(-0.10731592879921 * x), x, 1.0)), 0.254829592)
	t_2 = Float64(Float64(t_1 / (exp(x) ^ x)) / t_0)
	return Float64(Float64(1.0 - (t_2 ^ 3.0)) / Float64(Float64(fma(Float64(t_1 / t_0), (exp(x) ^ Float64(-x)), 1.0) * t_2) + 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[Abs[x], $MachinePrecision] * 0.3275911 + -1.0), $MachinePrecision] * N[(N[(0.284496736 + N[(N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(-0.10731592879921 * x), $MachinePrecision] * x + 1.0), $MachinePrecision]), $MachinePrecision] + 0.254829592), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 / N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, N[(N[(1.0 - N[Power[t$95$2, 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(t$95$1 / t$95$0), $MachinePrecision] * N[Power[N[Exp[x], $MachinePrecision], (-x)], $MachinePrecision] + 1.0), $MachinePrecision] * t$95$2), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. flip-+ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\frac{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. associate-/r/ N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1} \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000} - 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}, \left|x\right| \cdot \frac{3275911}{10000000} - 1, \frac{31853699}{125000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

6. Applied rewrites 78.7%

   \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

8. Applied rewrites 78.8%

   \[\leadsto \color{blue}{\frac{1 - {\left(\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} + 0.284496736}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)}{{\left(e^{x}\right)}^{x}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{3}}{1 + \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} + 0.284496736}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)}{{\left(e^{x}\right)}^{x}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} + 0.284496736}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, {\left(e^{x}\right)}^{\left(-x\right)}, 1\right)}} \]

9. Final simplification 78.8%

   \[\leadsto \frac{1 - {\left(\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)}{{\left(e^{x}\right)}^{x}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{3}}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, {\left(e^{x}\right)}^{\left(-x\right)}, 1\right) \cdot \frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), \frac{0.284496736 + \frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}}{\mathsf{fma}\left(-0.10731592879921 \cdot x, x, 1\right)}, 0.254829592\right)}{{\left(e^{x}\right)}^{x}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1} \]
10. Add Preprocessing

Alternative 8: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ 1 - e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \cdot \frac{\frac{\frac{\left(\frac{1.061405429}{{t\_0}^{2}} + 1.421413741\right) - \frac{1.453152027}{t\_0}}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (-
    1.0
    (*
     (exp (* (- (fabs x)) (fabs x)))
     (/
      (+
       (/
        (+
         (/
          (- (+ (/ 1.061405429 (pow t_0 2.0)) 1.421413741) (/ 1.453152027 t_0))
          t_0)
         -0.284496736)
        t_0)
       0.254829592)
      t_0)))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	return 1.0 - (exp((-fabs(x) * fabs(x))) * ((((((((1.061405429 / pow(t_0, 2.0)) + 1.421413741) - (1.453152027 / t_0)) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	return Float64(1.0 - Float64(exp(Float64(Float64(-abs(x)) * abs(x))) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / (t_0 ^ 2.0)) + 1.421413741) - Float64(1.453152027 / t_0)) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[Exp[N[((-N[Abs[x], $MachinePrecision]) * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] + 1.421413741), $MachinePrecision] - N[(1.453152027 / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

5. Taylor expanded in x around 0

   \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\left(\frac{1421413741}{1000000000} + \frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
6. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\left(\frac{1421413741}{1000000000} + \frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. +-commutative N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\left(\frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}} + \frac{1421413741}{1000000000}\right)} - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lower-+.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\left(\frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}} + \frac{1421413741}{1000000000}\right)} - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. associate-*r/ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\color{blue}{\frac{\frac{1061405429}{1000000000} \cdot 1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\color{blue}{\frac{1061405429}{1000000000}}}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. lower-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\color{blue}{\frac{\frac{1061405429}{1000000000}}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-pow.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   8. +-commutative N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\color{blue}{\left(\frac{3275911}{10000000} \cdot \left|x\right| + 1\right)}}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   9. *-commutative N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   10. lower-fma.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\color{blue}{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   11. lower-fabs.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\color{blue}{\left|x\right|}, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{1453152027}{1000000000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   12. associate-*r/ N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \color{blue}{\frac{\frac{1453152027}{1000000000} \cdot 1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   13. metadata-eval N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\color{blue}{\frac{1453152027}{1000000000}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   14. lower-/.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \color{blue}{\frac{\frac{1453152027}{1000000000}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   15. +-commutative N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\frac{1453152027}{1000000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   16. *-commutative N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\frac{1453152027}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   17. lower-fma.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\left(\frac{\frac{1061405429}{1000000000}}{{\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{2}} + \frac{1421413741}{1000000000}\right) - \frac{\frac{1453152027}{1000000000}}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

7. Applied rewrites 78.8%

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

8. Final simplification 78.8%

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

Alternative 9: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)\\ 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{1.061405429}{t\_1}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), -1.453152027\right)}{t\_0} + 1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{\frac{t\_1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right)}} \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (fma (* x x) 0.10731592879921 -1.0)))
   (-
    1.0
    (*
     (/
      (+
       (/
        (+
         (/
          (+
           (/
            (fma
             (/ 1.061405429 t_1)
             (fma 0.3275911 (fabs x) -1.0)
             -1.453152027)
            t_0)
           1.421413741)
          t_0)
         -0.284496736)
        t_0)
       0.254829592)
      (/ t_1 (fma (fabs x) 0.3275911 -1.0)))
     (exp (* (- (fabs x)) (fabs x)))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma((x * x), 0.10731592879921, -1.0);
	return 1.0 - ((((((((fma((1.061405429 / t_1), fma(0.3275911, fabs(x), -1.0), -1.453152027) / t_0) + 1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / (t_1 / fma(fabs(x), 0.3275911, -1.0))) * exp((-fabs(x) * fabs(x))));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(Float64(x * x), 0.10731592879921, -1.0)
	return Float64(1.0 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(fma(Float64(1.061405429 / t_1), fma(0.3275911, abs(x), -1.0), -1.453152027) / t_0) + 1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / Float64(t_1 / fma(abs(x), 0.3275911, -1.0))) * exp(Float64(Float64(-abs(x)) * abs(x)))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] * 0.10731592879921 + -1.0), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$1), $MachinePrecision] * N[(0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision] + -1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$1 / N[(N[Abs[x], $MachinePrecision] * 0.3275911 + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-N[Abs[x], $MachinePrecision]) * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. flip-+ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\frac{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. associate-/r/ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1} \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000} - 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}, \left|x\right| \cdot \frac{3275911}{10000000} - 1, \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

6. Applied rewrites 78.7%

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), -1.453152027\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
7. Step-by-step derivation

   1. lift-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right|} + 1} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. flip-+ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\frac{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) - 1 \cdot 1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) - \color{blue}{1}}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) - \color{blue}{-1 \cdot -1}}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. lower-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\frac{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) - -1 \cdot -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) - \color{blue}{1}}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   8. sub-neg N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\color{blue}{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) + \left(\mathsf{neg}\left(1\right)\right)}}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   9. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\left(\frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right|\right) + \color{blue}{-1}}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   10. swap-sqr N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\color{blue}{\left(\frac{3275911}{10000000} \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \left|x\right|\right)} + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   11. metadata-eval N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\color{blue}{\frac{10731592879921}{100000000000000}} \cdot \left(\left|x\right| \cdot \left|x\right|\right) + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   12. lift-fabs.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(\color{blue}{\left|x\right|} \cdot \left|x\right|\right) + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   13. lift-fabs.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(\left|x\right| \cdot \color{blue}{\left|x\right|}\right) + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   14. sqr-abs N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \color{blue}{\left(x \cdot x\right)} + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   15. lift-*.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \color{blue}{\left(x \cdot x\right)} + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   16. *-commutative N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\color{blue}{\left(x \cdot x\right) \cdot \frac{10731592879921}{100000000000000}} + -1}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   17. lift-fma.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\color{blue}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}}{\frac{3275911}{10000000} \cdot \left|x\right| - 1}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   18. sub-neg N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + \left(\mathsf{neg}\left(1\right)\right)}}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   19. metadata-eval N/A

       \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{-1453152027}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\frac{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}{\frac{3275911}{10000000} \cdot \left|x\right| + \color{blue}{-1}}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

8. Applied rewrites 78.8%

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), -1.453152027\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\color{blue}{\frac{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right)}}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

9. Final simplification 78.8%

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), -1.453152027\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\frac{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right)}} \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \]
10. Add Preprocessing

Alternative 10: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{0.3275911 \cdot \left|x\right| + 1}\\ t_1 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ 1 - \left(\left(\left(\frac{\frac{\frac{1.061405429}{t\_1} + -1.453152027}{t\_1} + 1.421413741}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right) + -0.284496736\right) \cdot t\_0 + 0.254829592\right) \cdot t\_0\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)))
        (t_1 (fma 0.3275911 (fabs x) 1.0)))
   (-
    1.0
    (*
     (*
      (+
       (*
        (+
         (*
          (/
           (+ (/ (+ (/ 1.061405429 t_1) -1.453152027) t_1) 1.421413741)
           (fma (* x x) 0.10731592879921 -1.0))
          (fma 0.3275911 (fabs x) -1.0))
         -0.284496736)
        t_0)
       0.254829592)
      t_0)
     (exp (* (- (fabs x)) (fabs x)))))))

C

double code(double x) {
	double t_0 = 1.0 / ((0.3275911 * fabs(x)) + 1.0);
	double t_1 = fma(0.3275911, fabs(x), 1.0);
	return 1.0 - (((((((((((1.061405429 / t_1) + -1.453152027) / t_1) + 1.421413741) / fma((x * x), 0.10731592879921, -1.0)) * fma(0.3275911, fabs(x), -1.0)) + -0.284496736) * t_0) + 0.254829592) * t_0) * exp((-fabs(x) * fabs(x))));
}

Julia

function code(x)
	t_0 = Float64(1.0 / Float64(Float64(0.3275911 * abs(x)) + 1.0))
	t_1 = fma(0.3275911, abs(x), 1.0)
	return Float64(1.0 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_1) + -1.453152027) / t_1) + 1.421413741) / fma(Float64(x * x), 0.10731592879921, -1.0)) * fma(0.3275911, abs(x), -1.0)) + -0.284496736) * t_0) + 0.254829592) * t_0) * exp(Float64(Float64(-abs(x)) * abs(x)))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(1.0 / N[(N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$1), $MachinePrecision] + -1.453152027), $MachinePrecision] / t$95$1), $MachinePrecision] + 1.421413741), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * 0.10731592879921 + -1.0), $MachinePrecision]), $MachinePrecision] * N[(0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + -0.284496736), $MachinePrecision] * t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] * t$95$0), $MachinePrecision] * N[Exp[N[((-N[Abs[x], $MachinePrecision]) * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \color{blue}{\left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. +-commutative N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000} + \frac{-1453152027}{1000000000}\right)}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-*.f64 N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. lift-/.f64 N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot \frac{1061405429}{1000000000} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. frac-2neg N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)\right)}} \cdot \frac{1061405429}{1000000000} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. metadata-eval N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)\right)} \cdot \frac{1061405429}{1000000000} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. associate-*l/ N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\color{blue}{\frac{-1 \cdot \frac{1061405429}{1000000000}}{\mathsf{neg}\left(\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)\right)}} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   8. div-inv N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\color{blue}{\left(-1 \cdot \frac{1061405429}{1000000000}\right) \cdot \frac{1}{\mathsf{neg}\left(\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)\right)}} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   9. metadata-eval N/A

      \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\left(-1 \cdot \frac{1061405429}{1000000000}\right) \cdot \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)\right)} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   10. frac-2neg N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\left(-1 \cdot \frac{1061405429}{1000000000}\right) \cdot \color{blue}{\frac{-1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} + \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   11. lower-fma.f64 N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot \frac{1061405429}{1000000000}, \frac{-1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}, \frac{-1453152027}{1000000000}\right)}\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   12. metadata-eval N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \mathsf{fma}\left(\color{blue}{\frac{-1061405429}{1000000000}}, \frac{-1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}, \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   13. lower-/.f64 78.7

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

   14. lift-+.f64 N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \mathsf{fma}\left(\frac{-1061405429}{1000000000}, \frac{-1}{\color{blue}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}, \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   15. +-commutative N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \mathsf{fma}\left(\frac{-1061405429}{1000000000}, \frac{-1}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}}, \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   16. lift-*.f64 N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \mathsf{fma}\left(\frac{-1061405429}{1000000000}, \frac{-1}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right|} + 1}, \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   17. *-commutative N/A

       \[\leadsto 1 - \left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \mathsf{fma}\left(\frac{-1061405429}{1000000000}, \frac{-1}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1}, \frac{-1453152027}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   18. lower-fma.f64 78.7

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

4. Applied rewrites 78.7%

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

6. Applied rewrites 78.8%

   \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \color{blue}{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right)}\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

7. Final simplification 78.8%

   \[\leadsto 1 - \left(\left(\left(\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right) + -0.284496736\right) \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1} + 0.254829592\right) \cdot \frac{1}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \]
8. Add Preprocessing

Alternative 11: 79.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ 1 - e^{\left(-x\right) \cdot x} \cdot \frac{\mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{t\_0} + -1.453152027}{t\_0} + 1.421413741}{t\_0} + -0.284496736}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0)))
   (-
    1.0
    (*
     (exp (* (- x) x))
     (/
      (fma
       (/
        (+
         (/ (+ (/ (+ (/ 1.061405429 t_0) -1.453152027) t_0) 1.421413741) t_0)
         -0.284496736)
        (fma (* x x) 0.10731592879921 -1.0))
       (fma 0.3275911 (fabs x) -1.0)
       0.254829592)
      (fma (fabs x) 0.3275911 1.0))))))

C

double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	return 1.0 - (exp((-x * x)) * (fma((((((((1.061405429 / t_0) + -1.453152027) / t_0) + 1.421413741) / t_0) + -0.284496736) / fma((x * x), 0.10731592879921, -1.0)), fma(0.3275911, fabs(x), -1.0), 0.254829592) / fma(fabs(x), 0.3275911, 1.0)));
}

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	return Float64(1.0 - Float64(exp(Float64(Float64(-x) * x)) * Float64(fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) + -1.453152027) / t_0) + 1.421413741) / t_0) + -0.284496736) / fma(Float64(x * x), 0.10731592879921, -1.0)), fma(0.3275911, abs(x), -1.0), 0.254829592) / fma(abs(x), 0.3275911, 1.0))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] + -1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * 0.10731592879921 + -1.0), $MachinePrecision]), $MachinePrecision] * N[(0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. flip-+ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\frac{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. associate-/r/ N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1} \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000} - 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}, \left|x\right| \cdot \frac{3275911}{10000000} - 1, \frac{31853699}{125000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

6. Applied rewrites 78.7%

   \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\mathsf{fma}\left(\frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{31853699}{125000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\color{blue}{\left|x\right| \cdot \left|x\right|}} \]

   2. lift-fabs.f64 N/A

      \[\leadsto 1 - \frac{\mathsf{fma}\left(\frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{31853699}{125000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\color{blue}{\left|x\right|} \cdot \left|x\right|} \]

   3. lift-fabs.f64 N/A

      \[\leadsto 1 - \frac{\mathsf{fma}\left(\frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{31853699}{125000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \color{blue}{\left|x\right|}} \]

   4. sqr-abs N/A

      \[\leadsto 1 - \frac{\mathsf{fma}\left(\frac{\frac{-8890523}{31250000} + \frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, \frac{10731592879921}{100000000000000}, -1\right)}, \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, -1\right), \frac{31853699}{125000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\color{blue}{x \cdot x}} \]

   5. lift-*.f64 78.7

      \[\leadsto 1 - \frac{\mathsf{fma}\left(\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\color{blue}{x \cdot x}} \]

8. Applied rewrites 78.7%

   \[\leadsto 1 - \frac{\mathsf{fma}\left(\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\color{blue}{x \cdot x}} \]

9. Final simplification 78.7%

   \[\leadsto 1 - e^{\left(-x\right) \cdot x} \cdot \frac{\mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \]
10. Add Preprocessing

Alternative 12: 79.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ 1 - \frac{\frac{\frac{\mathsf{fma}\left(-\left(\frac{1.061405429}{t\_1} + -1.453152027\right), \frac{-1}{t\_1}, 1.421413741\right)}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_0} \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)) (t_1 (fma 0.3275911 (fabs x) 1.0)))
   (-
    1.0
    (*
     (/
      (+
       (/
        (+
         (/
          (fma
           (- (+ (/ 1.061405429 t_1) -1.453152027))
           (/ -1.0 t_1)
           1.421413741)
          t_0)
         -0.284496736)
        t_0)
       0.254829592)
      t_0)
     (exp (* (- (fabs x)) (fabs x)))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma(0.3275911, fabs(x), 1.0);
	return 1.0 - ((((((fma(-((1.061405429 / t_1) + -1.453152027), (-1.0 / t_1), 1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0) * exp((-fabs(x) * fabs(x))));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(0.3275911, abs(x), 1.0)
	return Float64(1.0 - Float64(Float64(Float64(Float64(Float64(Float64(fma(Float64(-Float64(Float64(1.061405429 / t_1) + -1.453152027)), Float64(-1.0 / t_1), 1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0) * exp(Float64(Float64(-abs(x)) * abs(x)))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(N[(N[(N[((-N[(N[(1.061405429 / t$95$1), $MachinePrecision] + -1.453152027), $MachinePrecision]) * N[(-1.0 / t$95$1), $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / t$95$0), $MachinePrecision] * N[Exp[N[((-N[Abs[x], $MachinePrecision]) * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. frac-2neg N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\frac{\mathsf{neg}\left(\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right)\right)}{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. div-inv N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\left(\mathsf{neg}\left(\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right)\right)\right) \cdot \frac{1}{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\mathsf{neg}\left(\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right)\right)\right) \cdot \frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. frac-2neg N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\mathsf{neg}\left(\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right)\right)\right) \cdot \color{blue}{\frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\left(\mathsf{neg}\left(\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right)\right)\right) \cdot \color{blue}{\frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   8. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}\right)\right), \frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{1421413741}{1000000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   9. lower-neg.f64 78.7

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

   10. lift-fma.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\mathsf{fma}\left(-\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} + \frac{-1453152027}{1000000000}\right), \frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{1421413741}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   11. *-commutative N/A

       \[\leadsto 1 - \frac{\frac{\frac{\mathsf{fma}\left(-\left(\frac{\frac{1061405429}{1000000000}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right|} + 1} + \frac{-1453152027}{1000000000}\right), \frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \frac{1421413741}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   12. lower-fma.f64 78.7

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

   13. lift-fma.f64 N/A

       \[\leadsto 1 - \frac{\frac{\frac{\mathsf{fma}\left(-\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}\right), \frac{-1}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}}, \frac{1421413741}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   14. *-commutative N/A

       \[\leadsto 1 - \frac{\frac{\frac{\mathsf{fma}\left(-\left(\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-1453152027}{1000000000}\right), \frac{-1}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right|} + 1}, \frac{1421413741}{1000000000}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   15. lower-fma.f64 78.7

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

6. Applied rewrites 78.7%

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

7. Final simplification 78.7%

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

Alternative 13: 79.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ 1 - \frac{\mathsf{fma}\left(\frac{-1}{t\_0}, \frac{\frac{\frac{1.061405429}{t\_0} + -1.453152027}{t\_0} + 1.421413741}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} + 0.284496736, 0.254829592\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0)))
   (-
    1.0
    (*
     (/
      (fma
       (/ -1.0 t_0)
       (+
        (/
         (+ (/ (+ (/ 1.061405429 t_0) -1.453152027) t_0) 1.421413741)
         (fma -0.3275911 (fabs x) -1.0))
        0.284496736)
       0.254829592)
      (fma (fabs x) 0.3275911 1.0))
     (exp (* (- (fabs x)) (fabs x)))))))

C

double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	return 1.0 - ((fma((-1.0 / t_0), ((((((1.061405429 / t_0) + -1.453152027) / t_0) + 1.421413741) / fma(-0.3275911, fabs(x), -1.0)) + 0.284496736), 0.254829592) / fma(fabs(x), 0.3275911, 1.0)) * exp((-fabs(x) * fabs(x))));
}

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	return Float64(1.0 - Float64(Float64(fma(Float64(-1.0 / t_0), Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) + -1.453152027) / t_0) + 1.421413741) / fma(-0.3275911, abs(x), -1.0)) + 0.284496736), 0.254829592) / fma(abs(x), 0.3275911, 1.0)) * exp(Float64(Float64(-abs(x)) * abs(x)))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(-1.0 / t$95$0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] + -1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.421413741), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + 0.284496736), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-N[Abs[x], $MachinePrecision]) * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. frac-2neg N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right)}{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. clear-num N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{1}{\frac{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}{\mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right)}}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. associate-/r/ N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{1}{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)} \cdot \left(\mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right)\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\color{blue}{\mathsf{neg}\left(-1\right)}}{\mathsf{neg}\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)} \cdot \left(\mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right)\right) + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. frac-2neg N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} \cdot \left(\mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right)\right) + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   8. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} \cdot \left(\mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right)\right) + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   9. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}, \mathsf{neg}\left(\left(\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}\right)\right), \frac{31853699}{125000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

6. Applied rewrites 78.7%

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

7. Final simplification 78.7%

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

Alternative 14: 79.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ 1 - e^{\left(-x\right) \cdot x} \cdot \frac{\frac{\frac{1.421413741 + \frac{-1.453152027 + \frac{1.061405429}{t\_0}}{t\_0}}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (-
    1.0
    (*
     (exp (* (- x) x))
     (/
      (+
       (/
        (+
         (/ (+ 1.421413741 (/ (+ -1.453152027 (/ 1.061405429 t_0)) t_0)) t_0)
         -0.284496736)
        t_0)
       0.254829592)
      t_0)))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	return 1.0 - (exp((-x * x)) * ((((((1.421413741 + ((-1.453152027 + (1.061405429 / t_0)) / t_0)) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	return Float64(1.0 - Float64(exp(Float64(Float64(-x) * x)) * Float64(Float64(Float64(Float64(Float64(Float64(1.421413741 + Float64(Float64(-1.453152027 + Float64(1.061405429 / t_0)) / t_0)) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(N[(N[(1.421413741 + N[(N[(-1.453152027 + N[(1.061405429 / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\color{blue}{\left|x\right| \cdot \left|x\right|}} \]

   2. lift-fabs.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\color{blue}{\left|x\right|} \cdot \left|x\right|} \]

   3. lift-fabs.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \color{blue}{\left|x\right|}} \]

   4. sqr-abs N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\color{blue}{x \cdot x}} \]

   5. lift-*.f64 78.7

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

6. Applied rewrites 78.7%

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

7. Final simplification 78.7%

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

Alternative 15: 78.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, -1\right), -1.061405429, -1.453152027\right)}{t\_0} + 1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_0} \cdot e^{\left(-\left|x\right|\right) \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (-
    1.0
    (*
     (/
      (+
       (/
        (+
         (/
          (+
           (/
            (fma (fma (fabs x) 0.3275911 -1.0) -1.061405429 -1.453152027)
            t_0)
           1.421413741)
          t_0)
         -0.284496736)
        t_0)
       0.254829592)
      t_0)
     (exp (* (- (fabs x)) (fabs x)))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	return 1.0 - ((((((((fma(fma(fabs(x), 0.3275911, -1.0), -1.061405429, -1.453152027) / t_0) + 1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0) * exp((-fabs(x) * fabs(x))));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	return Float64(1.0 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(fma(fma(abs(x), 0.3275911, -1.0), -1.061405429, -1.453152027) / t_0) + 1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / t_0) * exp(Float64(Float64(-abs(x)) * abs(x)))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Abs[x], $MachinePrecision] * 0.3275911 + -1.0), $MachinePrecision] * -1.061405429 + -1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / t$95$0), $MachinePrecision] * N[Exp[N[((-N[Abs[x], $MachinePrecision]) * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. flip-+ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\color{blue}{\frac{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. associate-/r/ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1} \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000} - 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{\frac{1061405429}{1000000000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}, \left|x\right| \cdot \frac{3275911}{10000000} - 1, \frac{-1453152027}{1000000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

6. Applied rewrites 78.7%

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{1.061405429}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), -1.453152027\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

7. Taylor expanded in x around 0

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{-1061405429}{1000000000} \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right| - 1\right) - \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
8. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\frac{-1061405429}{1000000000} \cdot \left(\frac{3275911}{10000000} \cdot \left|x\right| - 1\right) + \left(\mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\left(\frac{3275911}{10000000} \cdot \left|x\right| - 1\right) \cdot \frac{-1061405429}{1000000000}} + \left(\mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{3275911}{10000000} \cdot \left|x\right| - 1, \frac{-1061405429}{1000000000}, \mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. sub-neg N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + \left(\mathsf{neg}\left(1\right)\right)}, \frac{-1061405429}{1000000000}, \mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. *-commutative N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + \left(\mathsf{neg}\left(1\right)\right), \frac{-1061405429}{1000000000}, \mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. metadata-eval N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\left|x\right| \cdot \frac{3275911}{10000000} + \color{blue}{-1}, \frac{-1061405429}{1000000000}, \mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, -1\right)}, \frac{-1061405429}{1000000000}, \mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   8. lower-fabs.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left|x\right|}, \frac{3275911}{10000000}, -1\right), \frac{-1061405429}{1000000000}, \mathsf{neg}\left(\frac{1453152027}{1000000000}\right)\right)}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   9. metadata-eval 78.6

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

9. Applied rewrites 78.6%

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

10. Final simplification 78.6%

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

Alternative 16: 55.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{e^{\left(-x\right) \cdot x}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot 0.254829592 \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (- 1.0 (* (/ (exp (* (- x) x)) (fma (fabs x) 0.3275911 1.0)) 0.254829592)))

C

double code(double x) {
	return 1.0 - ((exp((-x * x)) / fma(fabs(x), 0.3275911, 1.0)) * 0.254829592);
}

Julia

function code(x)
	return Float64(1.0 - Float64(Float64(exp(Float64(Float64(-x) * x)) / fma(abs(x), 0.3275911, 1.0)) * 0.254829592))
end

Wolfram

code[x_] := N[(1.0 - N[(N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] / N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]), $MachinePrecision] * 0.254829592), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.7%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\left(\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-/.f64 N/A

      \[\leadsto 1 - \left(\left(\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right) \cdot \color{blue}{\frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. un-div-inv N/A

      \[\leadsto 1 - \color{blue}{\frac{\frac{31853699}{125000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-8890523}{31250000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{1421413741}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \left(\frac{-1453152027}{1000000000} + \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{1061405429}{1000000000}\right)\right)\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. lower-/.f64 78.7

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

4. Applied rewrites 78.7%

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

   1. lift-+.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   2. lift-/.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   3. lift-fma.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000} + 1}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   4. lift-*.f64 N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   5. flip-+ N/A

      \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\color{blue}{\frac{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   6. associate-/r/ N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1} \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000} - 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

   7. lower-fma.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000}\right) \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000}\right) - 1 \cdot 1}, \left|x\right| \cdot \frac{3275911}{10000000} - 1, \frac{31853699}{125000000}\right)}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

6. Applied rewrites 78.7%

   \[\leadsto 1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{-0.284496736 + \frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(x \cdot x, 0.10731592879921, -1\right)}, \mathsf{fma}\left(0.3275911, \left|x\right|, -1\right), 0.254829592\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

7. Taylor expanded in x around inf

   \[\leadsto 1 - \color{blue}{\frac{31853699}{125000000} \cdot \frac{e^{\mathsf{neg}\left({\left(\left|x\right|\right)}^{2}\right)}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \]
8. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto 1 - \color{blue}{\frac{e^{\mathsf{neg}\left({\left(\left|x\right|\right)}^{2}\right)}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000}} \]

   2. lower-*.f64 N/A

      \[\leadsto 1 - \color{blue}{\frac{e^{\mathsf{neg}\left({\left(\left|x\right|\right)}^{2}\right)}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000}} \]

   3. exp-neg N/A

      \[\leadsto 1 - \frac{\color{blue}{\frac{1}{e^{{\left(\left|x\right|\right)}^{2}}}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   4. unpow2 N/A

      \[\leadsto 1 - \frac{\frac{1}{e^{\color{blue}{\left|x\right| \cdot \left|x\right|}}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   5. sqr-abs N/A

      \[\leadsto 1 - \frac{\frac{1}{e^{\color{blue}{x \cdot x}}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   6. unpow2 N/A

      \[\leadsto 1 - \frac{\frac{1}{e^{\color{blue}{{x}^{2}}}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   7. exp-neg N/A

      \[\leadsto 1 - \frac{\color{blue}{e^{\mathsf{neg}\left({x}^{2}\right)}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   8. lower-/.f64 N/A

      \[\leadsto 1 - \color{blue}{\frac{e^{\mathsf{neg}\left({x}^{2}\right)}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \cdot \frac{31853699}{125000000} \]

   9. lower-exp.f64 N/A

      \[\leadsto 1 - \frac{\color{blue}{e^{\mathsf{neg}\left({x}^{2}\right)}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   10. unpow2 N/A

       \[\leadsto 1 - \frac{e^{\mathsf{neg}\left(\color{blue}{x \cdot x}\right)}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   11. distribute-lft-neg-in N/A

       \[\leadsto 1 - \frac{e^{\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot x}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   12. lower-*.f64 N/A

       \[\leadsto 1 - \frac{e^{\color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot x}}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   13. lower-neg.f64 N/A

       \[\leadsto 1 - \frac{e^{\color{blue}{\left(-x\right)} \cdot x}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \cdot \frac{31853699}{125000000} \]

   14. +-commutative N/A

       \[\leadsto 1 - \frac{e^{\left(-x\right) \cdot x}}{\color{blue}{\frac{3275911}{10000000} \cdot \left|x\right| + 1}} \cdot \frac{31853699}{125000000} \]

   15. *-commutative N/A

       \[\leadsto 1 - \frac{e^{\left(-x\right) \cdot x}}{\color{blue}{\left|x\right| \cdot \frac{3275911}{10000000}} + 1} \cdot \frac{31853699}{125000000} \]

   16. lower-fma.f64 N/A

       \[\leadsto 1 - \frac{e^{\left(-x\right) \cdot x}}{\color{blue}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} \cdot \frac{31853699}{125000000} \]

   17. lower-fabs.f64 55.2

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

9. Applied rewrites 55.2%

   \[\leadsto 1 - \color{blue}{\frac{e^{\left(-x\right) \cdot x}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot 0.254829592} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024304 
(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)))))))