Jmat.Real.erf

Percentage Accurate: 79.0% → 83.3%

Time: 9.4s

Alternatives: 14

Speedup: 1.1×

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: 79.0% 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: 83.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{x \cdot x}\\ t_1 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_2 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_1} - 1.453152027}{t\_1} - -1.421413741}{t\_1} + -0.284496736}{t\_1} + 0.254829592}{t\_1 \cdot t\_0}\\ t_3 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_4 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_3} - 1.453152027}{t\_3} - -1.421413741}{t\_3} + -0.284496736}{t\_3} + 0.254829592}{t\_0 \cdot t\_3}\\ t_5 := 1 + \left({t\_4}^{6} - -1 \cdot {t\_4}^{3}\right)\\ t_6 := \mathsf{fma}\left(t\_2, t\_2 + 1, 1\right)\\ \frac{\frac{1}{t\_5}}{t\_6} - \frac{\frac{{t\_4}^{9}}{t\_5}}{t\_6} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (exp (* x x)))
        (t_1 (fma (fabs x) 0.3275911 1.0))
        (t_2
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_1) 1.453152027) t_1) -1.421413741)
              t_1)
             -0.284496736)
            t_1)
           0.254829592)
          (* t_1 t_0)))
        (t_3 (fma 0.3275911 (fabs x) 1.0))
        (t_4
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_3) 1.453152027) t_3) -1.421413741)
              t_3)
             -0.284496736)
            t_3)
           0.254829592)
          (* t_0 t_3)))
        (t_5 (+ 1.0 (- (pow t_4 6.0) (* -1.0 (pow t_4 3.0)))))
        (t_6 (fma t_2 (+ t_2 1.0) 1.0)))
   (- (/ (/ 1.0 t_5) t_6) (/ (/ (pow t_4 9.0) t_5) t_6))))

C

double code(double x) {
	double t_0 = exp((x * x));
	double t_1 = fma(fabs(x), 0.3275911, 1.0);
	double t_2 = ((((((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_1) + -0.284496736) / t_1) + 0.254829592) / (t_1 * t_0);
	double t_3 = fma(0.3275911, fabs(x), 1.0);
	double t_4 = ((((((((1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / (t_0 * t_3);
	double t_5 = 1.0 + (pow(t_4, 6.0) - (-1.0 * pow(t_4, 3.0)));
	double t_6 = fma(t_2, (t_2 + 1.0), 1.0);
	return ((1.0 / t_5) / t_6) - ((pow(t_4, 9.0) / t_5) / t_6);
}

Julia

function code(x)
	t_0 = exp(Float64(x * x))
	t_1 = fma(abs(x), 0.3275911, 1.0)
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_1) + -0.284496736) / t_1) + 0.254829592) / Float64(t_1 * t_0))
	t_3 = fma(0.3275911, abs(x), 1.0)
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / Float64(t_0 * t_3))
	t_5 = Float64(1.0 + Float64((t_4 ^ 6.0) - Float64(-1.0 * (t_4 ^ 3.0))))
	t_6 = fma(t_2, Float64(t_2 + 1.0), 1.0)
	return Float64(Float64(Float64(1.0 / t_5) / t_6) - Float64(Float64((t_4 ^ 9.0) / t_5) / t_6))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$1), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$1), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$1), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$1), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$1 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$3), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$3), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$3), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(1.0 + N[(N[Power[t$95$4, 6.0], $MachinePrecision] - N[(-1.0 * N[Power[t$95$4, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 * N[(t$95$2 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]}, N[(N[(N[(1.0 / t$95$5), $MachinePrecision] / t$95$6), $MachinePrecision] - N[(N[(N[Power[t$95$4, 9.0], $MachinePrecision] / t$95$5), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.2%

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

7. Applied rewrites 80.3%

   \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

9. Applied rewrites 83.3%

   \[\leadsto \color{blue}{\frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} - -1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} - \frac{\frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} - -1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)}} \]
10. Add Preprocessing

Alternative 2: 80.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_2 := e^{x \cdot x}\\ t_3 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_1} - 1.453152027}{t\_1} - -1.421413741}{t\_1} + -0.284496736}{t\_1} + 0.254829592}{t\_2 \cdot t\_1}\\ t_4 := \frac{1.061405429}{t\_0}\\ t_5 := 1 + \left({t\_3}^{6} + 1 \cdot {t\_3}^{3}\right)\\ t_6 := \frac{\frac{\frac{\frac{\frac{t\_4 \cdot t\_4 - 2.111650813574209}{t\_4 + 1.453152027}}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_0 \cdot t\_2}\\ \frac{\frac{1}{t\_5} - \frac{{t\_3}^{9}}{t\_5}}{\mathsf{fma}\left(t\_6, t\_6 + 1, 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (fma 0.3275911 (fabs x) 1.0))
        (t_2 (exp (* x x)))
        (t_3
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_1) 1.453152027) t_1) -1.421413741)
              t_1)
             -0.284496736)
            t_1)
           0.254829592)
          (* t_2 t_1)))
        (t_4 (/ 1.061405429 t_0))
        (t_5 (+ 1.0 (+ (pow t_3 6.0) (* 1.0 (pow t_3 3.0)))))
        (t_6
         (/
          (+
           (/
            (+
             (/
              (-
               (/
                (/ (- (* t_4 t_4) 2.111650813574209) (+ t_4 1.453152027))
                t_0)
               -1.421413741)
              t_0)
             -0.284496736)
            t_0)
           0.254829592)
          (* t_0 t_2))))
   (/ (- (/ 1.0 t_5) (/ (pow t_3 9.0) t_5)) (fma t_6 (+ t_6 1.0) 1.0))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = fma(0.3275911, fabs(x), 1.0);
	double t_2 = exp((x * x));
	double t_3 = ((((((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_1) + -0.284496736) / t_1) + 0.254829592) / (t_2 * t_1);
	double t_4 = 1.061405429 / t_0;
	double t_5 = 1.0 + (pow(t_3, 6.0) + (1.0 * pow(t_3, 3.0)));
	double t_6 = (((((((((t_4 * t_4) - 2.111650813574209) / (t_4 + 1.453152027)) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / (t_0 * t_2);
	return ((1.0 / t_5) - (pow(t_3, 9.0) / t_5)) / fma(t_6, (t_6 + 1.0), 1.0);
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(0.3275911, abs(x), 1.0)
	t_2 = exp(Float64(x * x))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_1) + -0.284496736) / t_1) + 0.254829592) / Float64(t_2 * t_1))
	t_4 = Float64(1.061405429 / t_0)
	t_5 = Float64(1.0 + Float64((t_3 ^ 6.0) + Float64(1.0 * (t_3 ^ 3.0))))
	t_6 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(t_4 * t_4) - 2.111650813574209) / Float64(t_4 + 1.453152027)) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / Float64(t_0 * t_2))
	return Float64(Float64(Float64(1.0 / t_5) - Float64((t_3 ^ 9.0) / t_5)) / fma(t_6, Float64(t_6 + 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$1), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$1), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$1), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$1), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.061405429 / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(1.0 + N[(N[Power[t$95$3, 6.0], $MachinePrecision] + N[(1.0 * N[Power[t$95$3, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(t$95$4 * t$95$4), $MachinePrecision] - 2.111650813574209), $MachinePrecision] / N[(t$95$4 + 1.453152027), $MachinePrecision]), $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 * t$95$2), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 / t$95$5), $MachinePrecision] - N[(N[Power[t$95$3, 9.0], $MachinePrecision] / t$95$5), $MachinePrecision]), $MachinePrecision] / N[(t$95$6 * N[(t$95$6 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.2%

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

7. Applied rewrites 80.3%

   \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]
8. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   2. flip-- N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   4. lower--.f64 N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   5. lower-*.f64 N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   6. metadata-eval N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \color{blue}{\frac{2111650813574208729}{1000000000000000000}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   7. lower-+.f64 80.3

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 2.111650813574209}{\color{blue}{\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}}, \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}} + 1, 1\right)} \]

9. Applied rewrites 80.3%

   \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 2.111650813574209}{\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}}, \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}} + 1, 1\right)} \]
10. Step-by-step derivation

    1. lift--.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{2111650813574208729}{1000000000000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    2. flip-- N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{2111650813574208729}{1000000000000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    3. lower-/.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{2111650813574208729}{1000000000000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    4. lower--.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{2111650813574208729}{1000000000000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    5. lower-*.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{2111650813574208729}{1000000000000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)}} - \frac{1453152027}{1000000000} \cdot \frac{1453152027}{1000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    6. metadata-eval N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{2111650813574208729}{1000000000000000000}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} \cdot \frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \color{blue}{\frac{2111650813574208729}{1000000000000000000}}}{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{1453152027}{1000000000}}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    7. lower-+.f64 80.3

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 2.111650813574209}{\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}}, \frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 2.111650813574209}{\color{blue}{\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}} + 1, 1\right)} \]

11. Applied rewrites 80.3%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 2.111650813574209}{\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}}, \frac{\frac{\frac{\frac{\color{blue}{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} \cdot \frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 2.111650813574209}{\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}} + 1, 1\right)} \]
12. Add Preprocessing

Alternative 3: 80.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := e^{x \cdot x}\\ t_2 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_1 \cdot t\_0}\\ t_3 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_4 := 1 + \left({t\_2}^{6} + 1 \cdot {t\_2}^{3}\right)\\ t_5 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_3} - 1.453152027}{t\_3} - -1.421413741}{t\_3} + -0.284496736}{t\_3} + 0.254829592}{t\_3 \cdot t\_1}\\ \frac{\frac{1}{t\_4} - \frac{{t\_2}^{9}}{t\_4}}{\mathsf{fma}\left(t\_5, t\_5 + 1, 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0))
        (t_1 (exp (* x x)))
        (t_2
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741)
              t_0)
             -0.284496736)
            t_0)
           0.254829592)
          (* t_1 t_0)))
        (t_3 (fma (fabs x) 0.3275911 1.0))
        (t_4 (+ 1.0 (+ (pow t_2 6.0) (* 1.0 (pow t_2 3.0)))))
        (t_5
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_3) 1.453152027) t_3) -1.421413741)
              t_3)
             -0.284496736)
            t_3)
           0.254829592)
          (* t_3 t_1))))
   (/ (- (/ 1.0 t_4) (/ (pow t_2 9.0) t_4)) (fma t_5 (+ t_5 1.0) 1.0))))

C

double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	double t_1 = exp((x * x));
	double t_2 = ((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / (t_1 * t_0);
	double t_3 = fma(fabs(x), 0.3275911, 1.0);
	double t_4 = 1.0 + (pow(t_2, 6.0) + (1.0 * pow(t_2, 3.0)));
	double t_5 = ((((((((1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / (t_3 * t_1);
	return ((1.0 / t_4) - (pow(t_2, 9.0) / t_4)) / fma(t_5, (t_5 + 1.0), 1.0);
}

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = exp(Float64(x * x))
	t_2 = 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_1 * t_0))
	t_3 = fma(abs(x), 0.3275911, 1.0)
	t_4 = Float64(1.0 + Float64((t_2 ^ 6.0) + Float64(1.0 * (t_2 ^ 3.0))))
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / Float64(t_3 * t_1))
	return Float64(Float64(Float64(1.0 / t_4) - Float64((t_2 ^ 9.0) / t_4)) / fma(t_5, Float64(t_5 + 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = 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$1 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(N[Power[t$95$2, 6.0], $MachinePrecision] + N[(1.0 * N[Power[t$95$2, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$3), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$3), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$3), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 / t$95$4), $MachinePrecision] - N[(N[Power[t$95$2, 9.0], $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] / N[(t$95$5 * N[(t$95$5 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.2%

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

7. Applied rewrites 80.3%

   \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]
8. Add Preprocessing

Alternative 4: 79.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := 1 + x \cdot x\\ t_2 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_1 \cdot t\_0}\\ t_3 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_4 := 1 + \left({t\_2}^{6} + 1 \cdot {t\_2}^{3}\right)\\ t_5 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_3} - 1.453152027}{t\_3} - -1.421413741}{t\_3} + -0.284496736}{t\_3} + 0.254829592}{t\_3 \cdot t\_1}\\ \frac{\frac{1}{t\_4} - \frac{{t\_2}^{9}}{t\_4}}{\mathsf{fma}\left(t\_5, t\_5 + 1, 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0))
        (t_1 (+ 1.0 (* x x)))
        (t_2
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741)
              t_0)
             -0.284496736)
            t_0)
           0.254829592)
          (* t_1 t_0)))
        (t_3 (fma (fabs x) 0.3275911 1.0))
        (t_4 (+ 1.0 (+ (pow t_2 6.0) (* 1.0 (pow t_2 3.0)))))
        (t_5
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_3) 1.453152027) t_3) -1.421413741)
              t_3)
             -0.284496736)
            t_3)
           0.254829592)
          (* t_3 t_1))))
   (/ (- (/ 1.0 t_4) (/ (pow t_2 9.0) t_4)) (fma t_5 (+ t_5 1.0) 1.0))))

C

double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	double t_1 = 1.0 + (x * x);
	double t_2 = ((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / (t_1 * t_0);
	double t_3 = fma(fabs(x), 0.3275911, 1.0);
	double t_4 = 1.0 + (pow(t_2, 6.0) + (1.0 * pow(t_2, 3.0)));
	double t_5 = ((((((((1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / (t_3 * t_1);
	return ((1.0 / t_4) - (pow(t_2, 9.0) / t_4)) / fma(t_5, (t_5 + 1.0), 1.0);
}

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = Float64(1.0 + Float64(x * x))
	t_2 = 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_1 * t_0))
	t_3 = fma(abs(x), 0.3275911, 1.0)
	t_4 = Float64(1.0 + Float64((t_2 ^ 6.0) + Float64(1.0 * (t_2 ^ 3.0))))
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / Float64(t_3 * t_1))
	return Float64(Float64(Float64(1.0 / t_4) - Float64((t_2 ^ 9.0) / t_4)) / fma(t_5, Float64(t_5 + 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$1 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 + N[(N[Power[t$95$2, 6.0], $MachinePrecision] + N[(1.0 * N[Power[t$95$2, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$3), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$3), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$3), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 / t$95$4), $MachinePrecision] - N[(N[Power[t$95$2, 9.0], $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] / N[(t$95$5 * N[(t$95$5 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.2%

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

7. Applied rewrites 80.3%

   \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

8. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\left(1 + {x}^{2}\right)} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]
9. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + \color{blue}{{x}^{2}}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   2. pow2 N/A

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

   3. lift-*.f64 80.0

      \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

10. Applied rewrites 80.0%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\color{blue}{\left(1 + x \cdot x\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

11. Taylor expanded in x around 0

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\left(1 + {x}^{2}\right)} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]
12. Step-by-step derivation

    1. lower-+.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + \color{blue}{{x}^{2}}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    2. pow2 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    3. lift-*.f64 79.9

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

13. Applied rewrites 79.9%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\color{blue}{\left(1 + x \cdot x\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

14. Taylor expanded in x around 0

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\left(1 + {x}^{2}\right)} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]
15. Step-by-step derivation

    1. lower-+.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + \color{blue}{{x}^{2}}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    2. pow2 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    3. lift-*.f64 79.9

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

16. Applied rewrites 79.9%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\color{blue}{\left(1 + x \cdot x\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

17. Taylor expanded in x around 0

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\left(1 + {x}^{2}\right)} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]
18. Step-by-step derivation

    1. lower-+.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + \color{blue}{{x}^{2}}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    2. pow2 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{e^{x \cdot x} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    3. lift-*.f64 79.9

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

19. Applied rewrites 79.9%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\color{blue}{\left(1 + x \cdot x\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

20. Taylor expanded in x around 0

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\color{blue}{\left(1 + {x}^{2}\right)} \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]
21. Step-by-step derivation

    1. lower-+.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + \color{blue}{{x}^{2}}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    2. pow2 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    3. lift-*.f64 79.9

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot \color{blue}{x}\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

22. Applied rewrites 79.9%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\color{blue}{\left(1 + x \cdot x\right)} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

23. Taylor expanded in x around 0

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \color{blue}{\left(1 + {x}^{2}\right)}}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]
24. Step-by-step derivation

    1. lower-+.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + \color{blue}{{x}^{2}}\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    2. pow2 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + x \cdot \color{blue}{x}\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

    3. lift-*.f64 79.7

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \left(1 + x \cdot \color{blue}{x}\right)}, \frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

25. Applied rewrites 79.7%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \color{blue}{\left(1 + x \cdot x\right)}}, \frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}} + 1, 1\right)} \]

26. Taylor expanded in x around 0

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + x \cdot x\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \color{blue}{\left(1 + {x}^{2}\right)}} + 1, 1\right)} \]
27. Step-by-step derivation

    1. lower-+.f64 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + x \cdot x\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + \color{blue}{{x}^{2}}\right)} + 1, 1\right)} \]

    2. pow2 N/A

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)} + \frac{31853699}{125000000}}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(\frac{3275911}{10000000}, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + x \cdot x\right)}, \frac{\frac{\frac{\frac{\frac{\frac{1061405429}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{1453152027}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} - \frac{-1421413741}{1000000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{-8890523}{31250000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right)} + \frac{31853699}{125000000}}{\mathsf{fma}\left(\left|x\right|, \frac{3275911}{10000000}, 1\right) \cdot \left(1 + x \cdot \color{blue}{x}\right)} + 1, 1\right)} \]

    3. lift-*.f64 79.7

       \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \left(1 + x \cdot x\right)}, \frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \left(1 + x \cdot \color{blue}{x}\right)} + 1, 1\right)} \]

28. Applied rewrites 79.7%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{\left(1 + x \cdot x\right) \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \left(1 + x \cdot x\right)}, \frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot \color{blue}{\left(1 + x \cdot x\right)}} + 1, 1\right)} \]
29. Add Preprocessing

Alternative 5: 79.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := e^{x \cdot x}\\ t_2 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_1 \cdot t\_0}\\ t_3 := {t\_2}^{6}\\ t_4 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_5 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_4} - 1.453152027}{t\_4} - -1.421413741}{t\_4} + -0.284496736}{t\_4} + 0.254829592}{t\_4 \cdot t\_1}\\ \frac{\frac{\frac{1 - t\_3 \cdot t\_3}{1 + t\_3}}{1 + {t\_2}^{3}}}{\mathsf{fma}\left(t\_5, t\_5 + 1, 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0))
        (t_1 (exp (* x x)))
        (t_2
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741)
              t_0)
             -0.284496736)
            t_0)
           0.254829592)
          (* t_1 t_0)))
        (t_3 (pow t_2 6.0))
        (t_4 (fma (fabs x) 0.3275911 1.0))
        (t_5
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_4) 1.453152027) t_4) -1.421413741)
              t_4)
             -0.284496736)
            t_4)
           0.254829592)
          (* t_4 t_1))))
   (/
    (/ (/ (- 1.0 (* t_3 t_3)) (+ 1.0 t_3)) (+ 1.0 (pow t_2 3.0)))
    (fma t_5 (+ t_5 1.0) 1.0))))

C

double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	double t_1 = exp((x * x));
	double t_2 = ((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / (t_1 * t_0);
	double t_3 = pow(t_2, 6.0);
	double t_4 = fma(fabs(x), 0.3275911, 1.0);
	double t_5 = ((((((((1.061405429 / t_4) - 1.453152027) / t_4) - -1.421413741) / t_4) + -0.284496736) / t_4) + 0.254829592) / (t_4 * t_1);
	return (((1.0 - (t_3 * t_3)) / (1.0 + t_3)) / (1.0 + pow(t_2, 3.0))) / fma(t_5, (t_5 + 1.0), 1.0);
}

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = exp(Float64(x * x))
	t_2 = 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_1 * t_0))
	t_3 = t_2 ^ 6.0
	t_4 = fma(abs(x), 0.3275911, 1.0)
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_4) - 1.453152027) / t_4) - -1.421413741) / t_4) + -0.284496736) / t_4) + 0.254829592) / Float64(t_4 * t_1))
	return Float64(Float64(Float64(Float64(1.0 - Float64(t_3 * t_3)) / Float64(1.0 + t_3)) / Float64(1.0 + (t_2 ^ 3.0))) / fma(t_5, Float64(t_5 + 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = 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$1 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[t$95$2, 6.0], $MachinePrecision]}, Block[{t$95$4 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$4), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$4), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$4), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$4), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$4 * t$95$1), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(1.0 - N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$3), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[Power[t$95$2, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$5 * N[(t$95$5 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.1%

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

7. Applied rewrites 79.3%

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

Alternative 6: 79.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)\\ t_1 := e^{x \cdot x}\\ t_2 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{t\_1 \cdot t\_0}\\ t_3 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_4 := \frac{\frac{\frac{\frac{\frac{1.061405429}{t\_3} - 1.453152027}{t\_3} - -1.421413741}{t\_3} + -0.284496736}{t\_3} + 0.254829592}{t\_3 \cdot t\_1}\\ \frac{\frac{1 - {t\_2}^{9}}{1 + \left({t\_2}^{6} - -1 \cdot {t\_2}^{3}\right)}}{\mathsf{fma}\left(t\_4, t\_4 + 1, 1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma 0.3275911 (fabs x) 1.0))
        (t_1 (exp (* x x)))
        (t_2
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741)
              t_0)
             -0.284496736)
            t_0)
           0.254829592)
          (* t_1 t_0)))
        (t_3 (fma (fabs x) 0.3275911 1.0))
        (t_4
         (/
          (+
           (/
            (+
             (/
              (- (/ (- (/ 1.061405429 t_3) 1.453152027) t_3) -1.421413741)
              t_3)
             -0.284496736)
            t_3)
           0.254829592)
          (* t_3 t_1))))
   (/
    (/ (- 1.0 (pow t_2 9.0)) (+ 1.0 (- (pow t_2 6.0) (* -1.0 (pow t_2 3.0)))))
    (fma t_4 (+ t_4 1.0) 1.0))))

C

double code(double x) {
	double t_0 = fma(0.3275911, fabs(x), 1.0);
	double t_1 = exp((x * x));
	double t_2 = ((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / (t_1 * t_0);
	double t_3 = fma(fabs(x), 0.3275911, 1.0);
	double t_4 = ((((((((1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / (t_3 * t_1);
	return ((1.0 - pow(t_2, 9.0)) / (1.0 + (pow(t_2, 6.0) - (-1.0 * pow(t_2, 3.0))))) / fma(t_4, (t_4 + 1.0), 1.0);
}

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = exp(Float64(x * x))
	t_2 = 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_1 * t_0))
	t_3 = fma(abs(x), 0.3275911, 1.0)
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / Float64(t_3 * t_1))
	return Float64(Float64(Float64(1.0 - (t_2 ^ 9.0)) / Float64(1.0 + Float64((t_2 ^ 6.0) - Float64(-1.0 * (t_2 ^ 3.0))))) / fma(t_4, Float64(t_4 + 1.0), 1.0))
end

Wolfram

code[x_] := Block[{t$95$0 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = 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$1 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$3), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$3), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$3), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(t$95$3 * t$95$1), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 - N[Power[t$95$2, 9.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$2, 6.0], $MachinePrecision] - N[(-1.0 * N[Power[t$95$2, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$4 * N[(t$95$4 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.2%

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

7. Applied rewrites 80.3%

   \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)} - \frac{{\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} + 1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)} \]

9. Applied rewrites 79.2%

   \[\leadsto \color{blue}{\frac{\frac{1 - {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{9}}{1 + \left({\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{6} - -1 \cdot {\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - 1.453152027}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} - -1.421413741}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + -0.284496736}{\mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)} + 0.254829592}{e^{x \cdot x} \cdot \mathsf{fma}\left(0.3275911, \left|x\right|, 1\right)}\right)}^{3}\right)}}{\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right) \cdot e^{x \cdot x}}, \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}} + 1, 1\right)}} \]
10. Add Preprocessing

Alternative 7: 79.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

function code(x)
	t_0 = fma(0.3275911, abs(x), 1.0)
	t_1 = exp(Float64(x * x))
	t_2 = 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_1 * t_0))
	t_3 = fma(abs(x), 0.3275911, 1.0)
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_3) - 1.453152027) / t_3) - -1.421413741) / t_3) + -0.284496736) / t_3) + 0.254829592) / Float64(t_3 * t_1))
	return Float64(Float64(Float64(1.0 - (t_2 ^ 6.0)) / Float64(1.0 + (t_2 ^ 3.0))) / fma(t_4, Float64(t_4 + 1.0), 1.0))
end

Wolfram

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

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

5. Applied rewrites 79.1%

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

7. Applied rewrites 79.1%

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

Alternative 8: 79.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(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]}, N[(N[(1.0 - N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * N[(t$95$1 + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

Alternative 9: 79.0% accurate, 1.1× speedup

Math

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

FPCore

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

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = fma(0.3275911, abs(x), 1.0)
	return Float64(1.0 - Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_1) - 1.453152027) / t_1) / t_1) - Float64(-1.421413741 / t_1)) + -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]}, Block[{t$95$1 = N[(0.3275911 * N[Abs[x], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(1.0 - N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$1), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(-1.421413741 / t$95$1), $MachinePrecision]), $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 79.0%

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

3. Applied rewrites 79.0%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

5. Applied rewrites 79.0%

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

Alternative 10: 79.0% 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 79.0%

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

3. Applied rewrites 79.0%

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

Alternative 11: 78.4% accurate, 1.4× speedup

Math

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

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 (fma x x 1.0))))))

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) / (t_0 * fma(x, x, 1.0)));
}

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

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.0%

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

4. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. pow2 N/A

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

   3. lower-fma.f64 78.4

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

6. Applied rewrites 78.4%

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

Alternative 12: 77.5% accurate, 1.5× speedup

Math

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

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 1.0)))))

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) / (t_0 * 1.0));
}

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(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / Float64(t_0 * 1.0)))
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[(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 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.0%

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

4. Taylor expanded in x around 0

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

6. Applied rewrites 77.5%

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

Alternative 13: 55.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{e^{-x \cdot x} \cdot \left(0.254829592 - \frac{0.284496736}{1 - -0.3275911 \cdot \left|x\right|}\right)}{1 + 0.3275911 \cdot \left|x\right|} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (-
  1.0
  (/
   (*
    (exp (- (* x x)))
    (- 0.254829592 (/ 0.284496736 (- 1.0 (* -0.3275911 (fabs x))))))
   (+ 1.0 (* 0.3275911 (fabs x))))))

C

double code(double x) {
	return 1.0 - ((exp(-(x * x)) * (0.254829592 - (0.284496736 / (1.0 - (-0.3275911 * fabs(x)))))) / (1.0 + (0.3275911 * 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
    code = 1.0d0 - ((exp(-(x * x)) * (0.254829592d0 - (0.284496736d0 / (1.0d0 - ((-0.3275911d0) * abs(x)))))) / (1.0d0 + (0.3275911d0 * abs(x))))
end function

Java

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

Python

def code(x):
	return 1.0 - ((math.exp(-(x * x)) * (0.254829592 - (0.284496736 / (1.0 - (-0.3275911 * math.fabs(x)))))) / (1.0 + (0.3275911 * math.fabs(x))))

Julia

function code(x)
	return Float64(1.0 - Float64(Float64(exp(Float64(-Float64(x * x))) * Float64(0.254829592 - Float64(0.284496736 / Float64(1.0 - Float64(-0.3275911 * abs(x)))))) / Float64(1.0 + Float64(0.3275911 * abs(x)))))
end

MATLAB

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

Wolfram

code[x_] := N[(1.0 - N[(N[(N[Exp[(-N[(x * x), $MachinePrecision])], $MachinePrecision] * N[(0.254829592 - N[(0.284496736 / N[(1.0 - N[(-0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

4. Taylor expanded in x around inf

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 55.3%

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

7. Taylor expanded in x around 0

   \[\leadsto 1 - \frac{e^{-x \cdot x} \cdot \left(\frac{31853699}{125000000} - \frac{\frac{8890523}{31250000}}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\right)}{1 + \frac{3275911}{10000000} \cdot \left|x\right|} \]
8. Step-by-step derivation

   1. lower-/.f64 N/A

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

   2. lift-fabs.f64 N/A

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. lift-fabs.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-fabs.f64 N/A

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

   8. lift-*.f64 55.3

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

9. Applied rewrites 55.3%

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

Alternative 14: 54.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - -0.3275911 \cdot \left|x\right|\\ 1 - \frac{0.254829592 - 0.284496736 \cdot \frac{1}{t\_0}}{t\_0} \end{array} \end{array} \]

FPCore

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

C

double code(double x) {
	double t_0 = 1.0 - (-0.3275911 * fabs(x));
	return 1.0 - ((0.254829592 - (0.284496736 * (1.0 / t_0))) / t_0);
}

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 - ((-0.3275911d0) * abs(x))
    code = 1.0d0 - ((0.254829592d0 - (0.284496736d0 * (1.0d0 / t_0))) / t_0)
end function

Java

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

Python

def code(x):
	t_0 = 1.0 - (-0.3275911 * math.fabs(x))
	return 1.0 - ((0.254829592 - (0.284496736 * (1.0 / t_0))) / t_0)

Julia

function code(x)
	t_0 = Float64(1.0 - Float64(-0.3275911 * abs(x)))
	return Float64(1.0 - Float64(Float64(0.254829592 - Float64(0.284496736 * Float64(1.0 / t_0))) / t_0))
end

MATLAB

function tmp = code(x)
	t_0 = 1.0 - (-0.3275911 * abs(x));
	tmp = 1.0 - ((0.254829592 - (0.284496736 * (1.0 / t_0))) / t_0);
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[(0.254829592 - N[(0.284496736 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.0%

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

3. Applied rewrites 79.1%

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

4. Taylor expanded in x around inf

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

   1. lower-/.f64 N/A

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

6. Applied rewrites 55.3%

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

7. Taylor expanded in x around 0

   \[\leadsto 1 - \frac{\frac{31853699}{125000000} - \frac{8890523}{31250000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{\color{blue}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}} \]
8. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto 1 - \frac{\frac{31853699}{125000000} - \frac{8890523}{31250000} \cdot \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}}{1 + \color{blue}{\frac{3275911}{10000000} \cdot \left|x\right|}} \]

9. Applied rewrites 54.4%

   \[\leadsto 1 - \frac{0.254829592 - 0.284496736 \cdot \frac{1}{1 - -0.3275911 \cdot \left|x\right|}}{\color{blue}{1 - -0.3275911 \cdot \left|x\right|}} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025135 
(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)))))))