Jmat.Real.erf

Percentage Accurate: 79.3% → 80.5%

Time: 8.6s

Alternatives: 14

Speedup: 1.3×

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: 79.3% 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: 80.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({t\_0}^{-3}, 1.061405429, \frac{1.421413741}{t\_0}\right) - 0.284496736\right) - \frac{1.453152027}{t\_0 \cdot t\_0}}{t\_0}, 1\right)}{t\_0}\\ t_2 := \left(e^{\left(-x\right) \cdot x} \cdot 0.254829592\right) \cdot t\_1\\ t_3 := 1 + \left({t\_2}^{6} + {t\_2}^{3}\right)\\ t_4 := t\_1 \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\\ \frac{\frac{1}{t\_3} - \frac{e^{\left(\log t\_2 \cdot 3\right) \cdot 3}}{t\_3}}{1 + \left({t\_4}^{2} + 1 \cdot t\_4\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1
         (/
          (fma
           3.924191033512309
           (/
            (-
             (-
              (fma (pow t_0 -3.0) 1.061405429 (/ 1.421413741 t_0))
              0.284496736)
             (/ 1.453152027 (* t_0 t_0)))
            t_0)
           1.0)
          t_0))
        (t_2 (* (* (exp (* (- x) x)) 0.254829592) t_1))
        (t_3 (+ 1.0 (+ (pow t_2 6.0) (pow t_2 3.0))))
        (t_4 (* t_1 (* 0.254829592 (exp (- (* x x)))))))
   (/
    (- (/ 1.0 t_3) (/ (exp (* (* (log t_2) 3.0) 3.0)) t_3))
    (+ 1.0 (+ (pow t_4 2.0) (* 1.0 t_4))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma(3.924191033512309, (((fma(pow(t_0, -3.0), 1.061405429, (1.421413741 / t_0)) - 0.284496736) - (1.453152027 / (t_0 * t_0))) / t_0), 1.0) / t_0;
	double t_2 = (exp((-x * x)) * 0.254829592) * t_1;
	double t_3 = 1.0 + (pow(t_2, 6.0) + pow(t_2, 3.0));
	double t_4 = t_1 * (0.254829592 * exp(-(x * x)));
	return ((1.0 / t_3) - (exp(((log(t_2) * 3.0) * 3.0)) / t_3)) / (1.0 + (pow(t_4, 2.0) + (1.0 * t_4)));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(fma(3.924191033512309, Float64(Float64(Float64(fma((t_0 ^ -3.0), 1.061405429, Float64(1.421413741 / t_0)) - 0.284496736) - Float64(1.453152027 / Float64(t_0 * t_0))) / t_0), 1.0) / t_0)
	t_2 = Float64(Float64(exp(Float64(Float64(-x) * x)) * 0.254829592) * t_1)
	t_3 = Float64(1.0 + Float64((t_2 ^ 6.0) + (t_2 ^ 3.0)))
	t_4 = Float64(t_1 * Float64(0.254829592 * exp(Float64(-Float64(x * x)))))
	return Float64(Float64(Float64(1.0 / t_3) - Float64(exp(Float64(Float64(log(t_2) * 3.0) * 3.0)) / t_3)) / Float64(1.0 + Float64((t_4 ^ 2.0) + Float64(1.0 * t_4))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(3.924191033512309 * N[(N[(N[(N[(N[Power[t$95$0, -3.0], $MachinePrecision] * 1.061405429 + N[(1.421413741 / t$95$0), $MachinePrecision]), $MachinePrecision] - 0.284496736), $MachinePrecision] - N[(1.453152027 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * 0.254829592), $MachinePrecision] * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(N[Power[t$95$2, 6.0], $MachinePrecision] + N[Power[t$95$2, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * N[(0.254829592 * N[Exp[(-N[(x * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 / t$95$3), $MachinePrecision] - N[(N[Exp[N[(N[(N[Log[t$95$2], $MachinePrecision] * 3.0), $MachinePrecision] * 3.0), $MachinePrecision]], $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$4, 2.0], $MachinePrecision] + N[(1.0 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 3.924191033512309, 1\right)\right) \cdot 0.254829592\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

4. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 + 3.924191033512309 \cdot \frac{\mathsf{fma}\left(1.061405429, \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}, 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

8. Applied rewrites 79.3%

   \[\leadsto \color{blue}{\frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)}} \]

10. Applied rewrites 80.5%

    \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\left(e^{\left(-x\right) \cdot x} \cdot 0.254829592\right) \cdot \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{6} + {\left(\left(e^{\left(-x\right) \cdot x} \cdot 0.254829592\right) \cdot \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{3}\right)} - \frac{e^{\left(\log \left(\left(e^{\left(-x\right) \cdot x} \cdot 0.254829592\right) \cdot \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) \cdot 3\right) \cdot 3}}{1 + \left({\left(\left(e^{\left(-x\right) \cdot x} \cdot 0.254829592\right) \cdot \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{6} + {\left(\left(e^{\left(-x\right) \cdot x} \cdot 0.254829592\right) \cdot \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right)}^{3}\right)}}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]
11. Add Preprocessing

Alternative 2: 79.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{t\_0} + {t\_0}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{t\_0 \cdot t\_0}}{t\_0}, 1\right)}{t\_0} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\\ \frac{1 - {t\_1}^{3}}{1 + \left({t\_1}^{2} + 1 \cdot t\_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1
         (*
          (/
           (fma
            3.924191033512309
            (/
             (-
              (-
               (+ (/ 1.421413741 t_0) (* (pow t_0 -3.0) 1.061405429))
               0.284496736)
              (/ 1.453152027 (* t_0 t_0)))
             t_0)
            1.0)
           t_0)
          (* 0.254829592 (exp (- (* x x)))))))
   (/ (- 1.0 (pow t_1 3.0)) (+ 1.0 (+ (pow t_1 2.0) (* 1.0 t_1))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = (fma(3.924191033512309, (((((1.421413741 / t_0) + (pow(t_0, -3.0) * 1.061405429)) - 0.284496736) - (1.453152027 / (t_0 * t_0))) / t_0), 1.0) / t_0) * (0.254829592 * exp(-(x * x)));
	return (1.0 - pow(t_1, 3.0)) / (1.0 + (pow(t_1, 2.0) + (1.0 * t_1)));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(Float64(fma(3.924191033512309, Float64(Float64(Float64(Float64(Float64(1.421413741 / t_0) + Float64((t_0 ^ -3.0) * 1.061405429)) - 0.284496736) - Float64(1.453152027 / Float64(t_0 * t_0))) / t_0), 1.0) / t_0) * Float64(0.254829592 * exp(Float64(-Float64(x * x)))))
	return Float64(Float64(1.0 - (t_1 ^ 3.0)) / Float64(1.0 + Float64((t_1 ^ 2.0) + Float64(1.0 * t_1))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(3.924191033512309 * N[(N[(N[(N[(N[(1.421413741 / t$95$0), $MachinePrecision] + N[(N[Power[t$95$0, -3.0], $MachinePrecision] * 1.061405429), $MachinePrecision]), $MachinePrecision] - 0.284496736), $MachinePrecision] - N[(1.453152027 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(0.254829592 * N[Exp[(-N[(x * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 - N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$1, 2.0], $MachinePrecision] + N[(1.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 3.924191033512309, 1\right)\right) \cdot 0.254829592\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

4. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 + 3.924191033512309 \cdot \frac{\mathsf{fma}\left(1.061405429, \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}, 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

8. Applied rewrites 79.3%

   \[\leadsto \color{blue}{\frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)}} \]
9. Step-by-step derivation

   1. lift-fma.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 N/A

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

   4. lower-*.f64 79.3

      \[\leadsto \frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]

10. Applied rewrites 79.3%

    \[\leadsto \frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]
11. Step-by-step derivation

    1. lift-fma.f64 N/A

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

    2. +-commutative N/A

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

    3. lower-+.f64 N/A

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

    4. lower-*.f64 79.3

       \[\leadsto \frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]

12. Applied rewrites 79.3%

    \[\leadsto \frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]
13. Step-by-step derivation

    1. lift-fma.f64 N/A

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

    2. +-commutative N/A

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

    3. lower-+.f64 N/A

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

    4. lower-*.f64 79.3

       \[\leadsto \frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]

14. Applied rewrites 79.3%

    \[\leadsto \frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\left(\frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + {\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3} \cdot 1.061405429\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)} \]
15. Add Preprocessing

Alternative 3: 79.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({t\_0}^{-3}, 1.061405429, \frac{1.421413741}{t\_0}\right) - 0.284496736\right) - \frac{1.453152027}{t\_0 \cdot t\_0}}{t\_0}, 1\right)}{t\_0} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\\ \frac{1 - {t\_1}^{3}}{1 + \left({t\_1}^{2} + 1 \cdot t\_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1
         (*
          (/
           (fma
            3.924191033512309
            (/
             (-
              (-
               (fma (pow t_0 -3.0) 1.061405429 (/ 1.421413741 t_0))
               0.284496736)
              (/ 1.453152027 (* t_0 t_0)))
             t_0)
            1.0)
           t_0)
          (* 0.254829592 (exp (- (* x x)))))))
   (/ (- 1.0 (pow t_1 3.0)) (+ 1.0 (+ (pow t_1 2.0) (* 1.0 t_1))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = (fma(3.924191033512309, (((fma(pow(t_0, -3.0), 1.061405429, (1.421413741 / t_0)) - 0.284496736) - (1.453152027 / (t_0 * t_0))) / t_0), 1.0) / t_0) * (0.254829592 * exp(-(x * x)));
	return (1.0 - pow(t_1, 3.0)) / (1.0 + (pow(t_1, 2.0) + (1.0 * t_1)));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(Float64(fma(3.924191033512309, Float64(Float64(Float64(fma((t_0 ^ -3.0), 1.061405429, Float64(1.421413741 / t_0)) - 0.284496736) - Float64(1.453152027 / Float64(t_0 * t_0))) / t_0), 1.0) / t_0) * Float64(0.254829592 * exp(Float64(-Float64(x * x)))))
	return Float64(Float64(1.0 - (t_1 ^ 3.0)) / Float64(1.0 + Float64((t_1 ^ 2.0) + Float64(1.0 * t_1))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(3.924191033512309 * N[(N[(N[(N[(N[Power[t$95$0, -3.0], $MachinePrecision] * 1.061405429 + N[(1.421413741 / t$95$0), $MachinePrecision]), $MachinePrecision] - 0.284496736), $MachinePrecision] - N[(1.453152027 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(0.254829592 * N[Exp[(-N[(x * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 - N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$1, 2.0], $MachinePrecision] + N[(1.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 3.924191033512309, 1\right)\right) \cdot 0.254829592\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

4. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 + 3.924191033512309 \cdot \frac{\mathsf{fma}\left(1.061405429, \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}, 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

8. Applied rewrites 79.3%

   \[\leadsto \color{blue}{\frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{3}}{1 + \left({\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2} + 1 \cdot \left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)\right)}} \]
9. Add Preprocessing

Alternative 4: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({t\_0}^{-3}, 1.061405429, \frac{1.421413741}{t\_0}\right) - 0.284496736\right) - \frac{1.453152027}{t\_0 \cdot t\_0}}{t\_0}, 1\right)}{t\_0} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\\ \frac{1 - {t\_1}^{2}}{1 + t\_1} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1
         (*
          (/
           (fma
            3.924191033512309
            (/
             (-
              (-
               (fma (pow t_0 -3.0) 1.061405429 (/ 1.421413741 t_0))
               0.284496736)
              (/ 1.453152027 (* t_0 t_0)))
             t_0)
            1.0)
           t_0)
          (* 0.254829592 (exp (- (* x x)))))))
   (/ (- 1.0 (pow t_1 2.0)) (+ 1.0 t_1))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = (fma(3.924191033512309, (((fma(pow(t_0, -3.0), 1.061405429, (1.421413741 / t_0)) - 0.284496736) - (1.453152027 / (t_0 * t_0))) / t_0), 1.0) / t_0) * (0.254829592 * exp(-(x * x)));
	return (1.0 - pow(t_1, 2.0)) / (1.0 + t_1);
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(Float64(fma(3.924191033512309, Float64(Float64(Float64(fma((t_0 ^ -3.0), 1.061405429, Float64(1.421413741 / t_0)) - 0.284496736) - Float64(1.453152027 / Float64(t_0 * t_0))) / t_0), 1.0) / t_0) * Float64(0.254829592 * exp(Float64(-Float64(x * x)))))
	return Float64(Float64(1.0 - (t_1 ^ 2.0)) / Float64(1.0 + t_1))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(3.924191033512309 * N[(N[(N[(N[(N[Power[t$95$0, -3.0], $MachinePrecision] * 1.061405429 + N[(1.421413741 / t$95$0), $MachinePrecision]), $MachinePrecision] - 0.284496736), $MachinePrecision] - N[(1.453152027 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] + 1.0), $MachinePrecision] / t$95$0), $MachinePrecision] * N[(0.254829592 * N[Exp[(-N[(x * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 - N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 3.924191033512309, 1\right)\right) \cdot 0.254829592\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

4. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 + 3.924191033512309 \cdot \frac{\mathsf{fma}\left(1.061405429, \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}, 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

8. Applied rewrites 79.3%

   \[\leadsto \color{blue}{\frac{1 - {\left(\frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)\right)}^{2}}{1 + \frac{\mathsf{fma}\left(3.924191033512309, \frac{\left(\mathsf{fma}\left({\left(\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\right)}^{-3}, 1.061405429, \frac{1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - 0.284496736\right) - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 1\right)}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)}} \]
9. Add Preprocessing

Alternative 5: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 0.3275911 \cdot \left|x\right|\\ 1 - \left(\frac{1 + 3.924191033512309 \cdot \frac{\mathsf{fma}\left(1.061405429, \frac{1}{{t\_0}^{3}}, 1.421413741 \cdot \frac{1}{t\_0}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{t\_0}^{2}}\right)}{t\_0}}{t\_0} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 0.3275911 (fabs x)))))
   (-
    1.0
    (*
     (*
      (/
       (+
        1.0
        (*
         3.924191033512309
         (/
          (-
           (fma 1.061405429 (/ 1.0 (pow t_0 3.0)) (* 1.421413741 (/ 1.0 t_0)))
           (+ 0.284496736 (* 1.453152027 (/ 1.0 (pow t_0 2.0)))))
          t_0)))
       t_0)
      0.254829592)
     (exp (- (* (fabs x) (fabs x))))))))

C

double code(double x) {
	double t_0 = 1.0 + (0.3275911 * fabs(x));
	return 1.0 - ((((1.0 + (3.924191033512309 * ((fma(1.061405429, (1.0 / pow(t_0, 3.0)), (1.421413741 * (1.0 / t_0))) - (0.284496736 + (1.453152027 * (1.0 / pow(t_0, 2.0))))) / t_0))) / t_0) * 0.254829592) * exp(-(fabs(x) * fabs(x))));
}

Julia

function code(x)
	t_0 = Float64(1.0 + Float64(0.3275911 * abs(x)))
	return Float64(1.0 - Float64(Float64(Float64(Float64(1.0 + Float64(3.924191033512309 * Float64(Float64(fma(1.061405429, Float64(1.0 / (t_0 ^ 3.0)), Float64(1.421413741 * Float64(1.0 / t_0))) - Float64(0.284496736 + Float64(1.453152027 * Float64(1.0 / (t_0 ^ 2.0))))) / t_0))) / t_0) * 0.254829592) * exp(Float64(-Float64(abs(x) * abs(x))))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(1.0 + N[(3.924191033512309 * N[(N[(N[(1.061405429 * N[(1.0 / N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision] + N[(1.421413741 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.284496736 + N[(1.453152027 * N[(1.0 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] * 0.254829592), $MachinePrecision] * N[Exp[(-N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 3.924191033512309, 1\right)\right) \cdot 0.254829592\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

4. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 + 3.924191033512309 \cdot \frac{\mathsf{fma}\left(1.061405429, \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}, 1.421413741 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) - \left(0.284496736 + 1.453152027 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)}{1 + 0.3275911 \cdot \left|x\right|}}{1 + 0.3275911 \cdot \left|x\right|}} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
7. Add Preprocessing

Alternative 6: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ 1 - \left(\mathsf{fma}\left(\frac{3.924191033512309}{t\_0}, \frac{\frac{1.453152027 - \frac{1.061405429}{t\_0}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} - -1.421413741}{t\_0} - 0.284496736, 1\right) \cdot \frac{1}{t\_0}\right) \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (-
    1.0
    (*
     (*
      (fma
       (/ 3.924191033512309 t_0)
       (-
        (/
         (-
          (/
           (- 1.453152027 (/ 1.061405429 t_0))
           (fma -0.3275911 (fabs x) -1.0))
          -1.421413741)
         t_0)
        0.284496736)
       1.0)
      (/ 1.0 t_0))
     (* 0.254829592 (exp (- (* x x))))))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	return 1.0 - ((fma((3.924191033512309 / t_0), (((((1.453152027 - (1.061405429 / t_0)) / fma(-0.3275911, fabs(x), -1.0)) - -1.421413741) / t_0) - 0.284496736), 1.0) * (1.0 / t_0)) * (0.254829592 * exp(-(x * x))));
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	return Float64(1.0 - Float64(Float64(fma(Float64(3.924191033512309 / t_0), Float64(Float64(Float64(Float64(Float64(1.453152027 - Float64(1.061405429 / t_0)) / fma(-0.3275911, abs(x), -1.0)) - -1.421413741) / t_0) - 0.284496736), 1.0) * Float64(1.0 / t_0)) * Float64(0.254829592 * exp(Float64(-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[(3.924191033512309 / t$95$0), $MachinePrecision] * N[(N[(N[(N[(N[(1.453152027 - N[(1.061405429 / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] - 0.284496736), $MachinePrecision] + 1.0), $MachinePrecision] * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(0.254829592 * N[Exp[(-N[(x * x), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \mathsf{fma}\left(\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, 3.924191033512309, 1\right)\right) \cdot 0.254829592\right)} \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

5. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\left(\frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \color{blue}{\mathsf{fma}\left(\frac{\frac{1.453152027 - \frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 0.284496736, \frac{3.924191033512309}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}, 1\right)}\right) \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lower-*.f64 N/A

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

7. Applied rewrites 79.3%

   \[\leadsto 1 - \color{blue}{\left(\mathsf{fma}\left(\frac{3.924191033512309}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}, \frac{\frac{1.453152027 - \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 0.284496736, 1\right) \cdot \frac{1}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) \cdot \left(0.254829592 \cdot e^{-x \cdot x}\right)} \]
8. Add Preprocessing

Alternative 7: 79.3% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

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

5. Applied rewrites 79.3%

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

Alternative 8: 79.3% accurate, 1.2× speedup

Math

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

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)
      (exp (* 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) / exp((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) / exp(Float64(x * x))) * Float64(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[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

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

Alternative 9: 79.3% accurate, 1.3× speedup

Math

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

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

Derivation

1. Initial program 79.3%

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

3. Applied rewrites 79.3%

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

Alternative 10: 79.3% 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 79.3%

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

3. Applied rewrites 79.3%

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

Alternative 11: 79.3% 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 79.3%

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

3. Applied rewrites 79.3%

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

Alternative 12: 79.3% 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 79.3%

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

3. Applied rewrites 79.3%

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

Alternative 13: 55.9% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.3%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

5. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(0.254829592 + \color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

7. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(0.254829592 + \frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(-0.284496736 + \color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

9. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(0.254829592 + \frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(-0.284496736 + \frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(1.421413741 + \color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

    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 79.3

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

11. Applied rewrites 79.3%

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

12. Taylor expanded in x around inf

    \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot \frac{3275911}{10000000}}{1 - \frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right)} \cdot \color{blue}{\frac{31853699}{125000000}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
13. Step-by-step derivation

14. Applied rewrites 55.9%

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

16. Applied rewrites 55.9%

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

Alternative 14: 55.9% accurate, 3.3× speedup

Math

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

FPCore

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

C

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

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
    code = 1.0d0 - (exp((-x * x)) * (0.254829592d0 * (1.0d0 - (abs(x) * 0.3275911d0))))
end function

Java

public static double code(double x) {
	return 1.0 - (Math.exp((-x * x)) * (0.254829592 * (1.0 - (Math.abs(x) * 0.3275911))));
}

Python

def code(x):
	return 1.0 - (math.exp((-x * x)) * (0.254829592 * (1.0 - (math.fabs(x) * 0.3275911))))

Julia

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

MATLAB

function tmp = code(x)
	tmp = 1.0 - (exp((-x * x)) * (0.254829592 * (1.0 - (abs(x) * 0.3275911))));
end

Wolfram

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

Derivation

1. Initial program 79.3%

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

3. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

5. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(0.254829592 + \color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

7. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(0.254829592 + \frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(-0.284496736 + \color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

   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 79.3

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

9. Applied rewrites 79.3%

   \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(0.254829592 + \frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(-0.284496736 + \frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)} \cdot \left(1.421413741 + \color{blue}{\frac{1 - \left|x\right| \cdot 0.3275911}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
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 79.3

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

    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 79.3

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

11. Applied rewrites 79.3%

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

12. Taylor expanded in x around inf

    \[\leadsto 1 - \left(\frac{1 - \left|x\right| \cdot \frac{3275911}{10000000}}{1 - \frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right)} \cdot \color{blue}{\frac{31853699}{125000000}}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
13. Step-by-step derivation

14. Applied rewrites 55.9%

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

15. Taylor expanded in x around 0

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

    1. lower--.f64 N/A

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

    2. lower-*.f64 N/A

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

    3. lower-fabs.f64 55.9

       \[\leadsto 1 - \left(\left(1 - 0.3275911 \cdot \left|x\right|\right) \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]

17. Applied rewrites 55.9%

    \[\leadsto 1 - \left(\color{blue}{\left(1 - 0.3275911 \cdot \left|x\right|\right)} \cdot 0.254829592\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \]
18. Step-by-step derivation

    1. lift-*.f64 N/A

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

19. Applied rewrites 55.9%

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

Reproduce

herbie shell --seed 2025148 
(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)))))))