Jmat.Real.erf

Percentage Accurate: 79.1% → 79.1%

Time: 7.5s

Alternatives: 12

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x)
use fmin_fmax_functions
    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: 79.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := e^{x \cdot x}\\ t_2 := \frac{\left(\mathsf{fma}\left({t\_0}^{-4}, 1.061405429, \frac{1.421413741}{t\_0 \cdot t\_0}\right) + 0.254829592\right) - \mathsf{fma}\left({t\_0}^{-3}, 1.453152027, \frac{0.284496736}{t\_0}\right)}{\mathsf{fma}\left(\left|x\right|, -0.3275911, -1\right) \cdot t\_1} - 1\\ t_3 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{t\_3} - 1.453152027}{t\_3} - -1.421413741}{t\_3} - 0.284496736}{t\_3} - -0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}}{t\_1}\right)}^{2}}{t\_2} - \frac{1}{t\_2} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (exp (* x x)))
        (t_2
         (-
          (/
           (-
            (+
             (fma (pow t_0 -4.0) 1.061405429 (/ 1.421413741 (* t_0 t_0)))
             0.254829592)
            (fma (pow t_0 -3.0) 1.453152027 (/ 0.284496736 t_0)))
           (* (fma (fabs x) -0.3275911 -1.0) t_1))
          1.0))
        (t_3 (fma 0.3275911 (fabs x) 1.0)))
   (-
    (/
     (pow
      (/
       (/
        (-
         (/
          (-
           (/ (- (/ (- (/ 1.061405429 t_3) 1.453152027) t_3) -1.421413741) t_3)
           0.284496736)
          t_3)
         -0.254829592)
        (fma -0.3275911 (fabs x) -1.0))
       t_1)
      2.0)
     t_2)
    (/ 1.0 t_2))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = exp((x * x));
	double t_2 = (((fma(pow(t_0, -4.0), 1.061405429, (1.421413741 / (t_0 * t_0))) + 0.254829592) - fma(pow(t_0, -3.0), 1.453152027, (0.284496736 / t_0))) / (fma(fabs(x), -0.3275911, -1.0) * t_1)) - 1.0;
	double t_3 = fma(0.3275911, fabs(x), 1.0);
	return (pow(((((((((((1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) - 0.284496736) / t_3) - -0.254829592) / fma(-0.3275911, fabs(x), -1.0)) / t_1), 2.0) / t_2) - (1.0 / t_2);
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = exp(Float64(x * x))
	t_2 = Float64(Float64(Float64(Float64(fma((t_0 ^ -4.0), 1.061405429, Float64(1.421413741 / Float64(t_0 * t_0))) + 0.254829592) - fma((t_0 ^ -3.0), 1.453152027, Float64(0.284496736 / t_0))) / Float64(fma(abs(x), -0.3275911, -1.0) * t_1)) - 1.0)
	t_3 = fma(0.3275911, abs(x), 1.0)
	return Float64(Float64((Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) - 0.284496736) / t_3) - -0.254829592) / fma(-0.3275911, abs(x), -1.0)) / t_1) ^ 2.0) / t_2) - Float64(1.0 / t_2))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[Power[t$95$0, -4.0], $MachinePrecision] * 1.061405429 + N[(1.421413741 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.254829592), $MachinePrecision] - N[(N[Power[t$95$0, -3.0], $MachinePrecision] * 1.453152027 + N[(0.284496736 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[Abs[x], $MachinePrecision] * -0.3275911 + -1.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(N[(N[Power[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$3), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$3), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] - 0.284496736), $MachinePrecision] / t$95$3), $MachinePrecision] - -0.254829592), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 2.0], $MachinePrecision] / t$95$2), $MachinePrecision] - N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.1%

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

6. Taylor expanded in x around inf

   \[\leadsto \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-31853699}{125000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)}}{e^{x \cdot x}}\right)}^{2}}{\color{blue}{\frac{e^{-1 \cdot {x}^{2}} \cdot \left(\left(\frac{31853699}{125000000} + \left(\frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{4}} + \frac{1421413741}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}\right)\right) - \left(\frac{8890523}{31250000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} + \frac{1453152027}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{3}}\right)\right)}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - 1}} - \frac{1}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-31853699}{125000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)}, e^{\left(-x\right) \cdot x}, -1\right)} \]

8. Applied rewrites 79.1%

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

9. Taylor expanded in x around inf

   \[\leadsto \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-31853699}{125000000}}{\mathsf{fma}\left(\frac{-3275911}{10000000}, \left|x\right|, -1\right)}}{e^{x \cdot x}}\right)}^{2}}{\frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{-4}, \frac{1061405429}{1000000000}, \frac{\frac{1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right) + \frac{31853699}{125000000}\right) - \mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)\right)}^{-3}, \frac{1453152027}{1000000000}, \frac{\frac{8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}\right)}{\mathsf{fma}\left(\left|x\right|, \frac{-3275911}{10000000}, -1\right) \cdot e^{x \cdot x}} - 1} - \frac{1}{\color{blue}{\frac{e^{-1 \cdot {x}^{2}} \cdot \left(\left(\frac{31853699}{125000000} + \left(\frac{1061405429}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{4}} + \frac{1421413741}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{2}}\right)\right) - \left(\frac{8890523}{31250000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} + \frac{1453152027}{1000000000} \cdot \frac{1}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{3}}\right)\right)}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - 1}} \]

11. Applied rewrites 79.1%

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

Alternative 2: 79.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.1%

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

Alternative 3: 79.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0
         (/
          (- 1.0 (* (fabs x) 0.3275911))
          (- 1.0 (* 0.10731592879921 (* x 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 - (fabs(x) * 0.3275911)) / (1.0 - (0.10731592879921 * (x * 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = (1.0d0 - (abs(x) * 0.3275911d0)) / (1.0d0 - (0.10731592879921d0 * (x * 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 - (Math.abs(x) * 0.3275911)) / (1.0 - (0.10731592879921 * (x * 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 - (math.fabs(x) * 0.3275911)) / (1.0 - (0.10731592879921 * (x * 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(Float64(1.0 - Float64(abs(x) * 0.3275911)) / Float64(1.0 - Float64(0.10731592879921 * Float64(x * 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 - (abs(x) * 0.3275911)) / (1.0 - (0.10731592879921 * (x * 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[(N[(1.0 - N[(N[Abs[x], $MachinePrecision] * 0.3275911), $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(0.10731592879921 * N[(x * 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]]

Derivation

1. Initial program 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

3. Applied rewrites 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

5. Applied rewrites 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

7. Applied rewrites 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

9. Applied rewrites 79.1%

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

    1. lift-/.f64 N/A

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

    2. lift-+.f64 N/A

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

    3. flip-+ N/A

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

    4. div-flip-rev N/A

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

    5. lower-/.f64 N/A

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

    6. lower--.f64 N/A

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

    7. lift-*.f64 N/A

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

    8. *-commutative N/A

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

    9. lower-*.f64 N/A

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

    10. metadata-eval N/A

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

    11. lower--.f64 N/A

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

    12. lift-*.f64 N/A

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

    13. lift-*.f64 N/A

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

    14. swap-sqr N/A

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

    15. lift-*.f64 N/A

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

    16. lower-*.f64 N/A

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

    17. metadata-eval 79.1

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

    18. lift-*.f64 N/A

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

    19. lift-fabs.f64 N/A

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

    20. lift-fabs.f64 N/A

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

    21. sqr-abs N/A

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

    22. lower-*.f64 79.1

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

11. Applied rewrites 79.1%

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

Alternative 4: 79.1% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

3. Applied rewrites 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

5. Applied rewrites 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

7. Applied rewrites 79.1%

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

   1. lift-/.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. flip-+ N/A

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

   4. div-flip-rev N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. metadata-eval N/A

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

   11. lower--.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. swap-sqr N/A

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

   15. lift-*.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. metadata-eval 79.1

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

   18. lift-*.f64 N/A

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

   19. lift-fabs.f64 N/A

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

   20. lift-fabs.f64 N/A

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

   21. sqr-abs N/A

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

   22. lower-*.f64 79.1

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

9. Applied rewrites 79.1%

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

    1. lift-/.f64 N/A

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

    2. lift-+.f64 N/A

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

    3. flip-+ N/A

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

    4. div-flip-rev N/A

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

    5. lower-/.f64 N/A

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

    6. lower--.f64 N/A

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

    7. lift-*.f64 N/A

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

    8. *-commutative N/A

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

    9. lower-*.f64 N/A

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

    10. metadata-eval N/A

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

    11. lower--.f64 N/A

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

    12. lift-*.f64 N/A

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

    13. lift-*.f64 N/A

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

    14. swap-sqr N/A

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

    15. lift-*.f64 N/A

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

    16. lower-*.f64 N/A

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

    17. metadata-eval 79.1

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

    18. lift-*.f64 N/A

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

    19. lift-fabs.f64 N/A

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

    20. lift-fabs.f64 N/A

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

    21. sqr-abs N/A

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

    22. lower-*.f64 79.1

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

11. Applied rewrites 79.1%

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

13. Applied rewrites 79.1%

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

Alternative 5: 79.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

Alternative 6: 79.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

   1. lift--.f64 N/A

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

   2. sub-flip N/A

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

   3. lift-/.f64 N/A

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

   4. mult-flip N/A

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

   5. lift-/.f64 N/A

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

   6. metadata-eval N/A

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

   7. lower-fma.f64 79.1

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

5. Applied rewrites 79.1%

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

Alternative 7: 79.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

   1. lift--.f64 N/A

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

   2. sub-flip N/A

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

   3. lift-/.f64 N/A

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

   4. mult-flip N/A

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

   5. lift-/.f64 N/A

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

   6. lower-fma.f64 N/A

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

   7. lift-fma.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-fma.f64 N/A

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

   10. metadata-eval 79.1

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

5. Applied rewrites 79.1%

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

Alternative 8: 79.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) - 0.284496736) / t_0) - -0.254829592) / exp(Float64(x * x))) / 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[(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] / t$95$0), $MachinePrecision] - -0.254829592), $MachinePrecision] / N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

Alternative 9: 79.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

Alternative 10: 79.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	return 1.0 - (((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) - 0.284496736) / t_0) - -0.254829592) / (t_0 * exp((x * 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(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) - 0.284496736) / t_0) - -0.254829592) / Float64(t_0 * exp(Float64(x * 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[(1.061405429 / t$95$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$0 * N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

Alternative 11: 78.5% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) - 0.284496736) / t_0) - -0.254829592) / fma(x, x, 1.0)) / 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[(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] / t$95$0), $MachinePrecision] - -0.254829592), $MachinePrecision] / N[(x * x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

4. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. pow2 N/A

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

   3. lower-fma.f64 78.5

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

6. Applied rewrites 78.5%

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -0.254829592}{\color{blue}{\mathsf{fma}\left(x, x, 1\right)}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \]
7. Add Preprocessing

Alternative 12: 77.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

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(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) - 0.284496736) / t_0) - -0.254829592) / 1.0) / 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[(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] / t$95$0), $MachinePrecision] - -0.254829592), $MachinePrecision] / 1.0), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.1%

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

3. Applied rewrites 79.1%

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

4. Taylor expanded in x around 0

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

6. Applied rewrites 77.5%

   \[\leadsto 1 - \frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -0.254829592}{\color{blue}{1}}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025140 
(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)))))))