Jmat.Real.erf

Percentage Accurate: 79.1% → 80.4%

Time: 15.2s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 80.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1}\\ t_1 := \left(t\_0 \cdot \left(0.254829592 + t\_0 \cdot \left(-0.284496736 + t\_0 \cdot \left(1.421413741 + t\_0 \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\\ t_2 := 1 + \left({t\_1}^{6} + {t\_1}^{3}\right)\\ \frac{\frac{1}{t\_2} - \frac{{t\_1}^{9}}{t\_2}}{1 + \mathsf{fma}\left(t\_1, t\_1, t\_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (* 0.3275911 (fabs x))) -1.0))
        (t_1
         (*
          (*
           t_0
           (+
            0.254829592
            (*
             t_0
             (+
              -0.284496736
              (*
               t_0
               (+
                1.421413741
                (*
                 t_0
                 (+
                  -1.453152027
                  (/
                   1.061405429
                   (/
                    (- (* 0.10731592879921 (* x x)) 1.0)
                    (- (* (fabs x) 0.3275911) 1.0)))))))))))
          (exp (* (- x) x))))
        (t_2 (+ 1.0 (+ (pow t_1 6.0) (pow t_1 3.0)))))
   (/ (- (/ 1.0 t_2) (/ (pow t_1 9.0) t_2)) (+ 1.0 (fma t_1 t_1 t_1)))))

C

double code(double x) {
	double t_0 = pow((1.0 + (0.3275911 * fabs(x))), -1.0);
	double t_1 = (t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (1.061405429 / (((0.10731592879921 * (x * x)) - 1.0) / ((fabs(x) * 0.3275911) - 1.0))))))))))) * exp((-x * x));
	double t_2 = 1.0 + (pow(t_1, 6.0) + pow(t_1, 3.0));
	return ((1.0 / t_2) - (pow(t_1, 9.0) / t_2)) / (1.0 + fma(t_1, t_1, t_1));
}

Julia

function code(x)
	t_0 = Float64(1.0 + Float64(0.3275911 * abs(x))) ^ -1.0
	t_1 = 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(1.061405429 / Float64(Float64(Float64(0.10731592879921 * Float64(x * x)) - 1.0) / Float64(Float64(abs(x) * 0.3275911) - 1.0))))))))))) * exp(Float64(Float64(-x) * x)))
	t_2 = Float64(1.0 + Float64((t_1 ^ 6.0) + (t_1 ^ 3.0)))
	return Float64(Float64(Float64(1.0 / t_2) - Float64((t_1 ^ 9.0) / t_2)) / Float64(1.0 + fma(t_1, t_1, t_1)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Power[N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]}, Block[{t$95$1 = 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[(1.061405429 / N[(N[(N[(0.10731592879921 * N[(x * x), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] / N[(N[(N[Abs[x], $MachinePrecision] * 0.3275911), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(N[Power[t$95$1, 6.0], $MachinePrecision] + N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 / t$95$2), $MachinePrecision] - N[(N[Power[t$95$1, 9.0], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$1 * t$95$1 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Initial program 76.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fabs.f64 N/A

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

   4. +-commutative N/A

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

   5. flip-+ N/A

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

   6. lower-/.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower--.f64 N/A

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

   9. lift-fabs.f64 N/A

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

   10. lift-fabs.f64 N/A

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

   11. swap-sqr N/A

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

   12. lift-*.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. metadata-eval N/A

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

   15. lift-*.f64 N/A

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

   16. lift-fabs.f64 N/A

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

   17. lift-fabs.f64 N/A

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

   18. sqr-abs N/A

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

   19. lower-*.f64 N/A

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

   20. lower--.f64 N/A

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

4. Applied rewrites 76.9%

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

6. Applied rewrites 77.0%

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

8. Applied rewrites 77.1%

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

10. Applied rewrites 78.3%

    \[\leadsto \frac{\color{blue}{\frac{1}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{6} + 1 \cdot {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)} - \frac{{\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{9}}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{6} + 1 \cdot {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}}{1 + \mathsf{fma}\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

11. Final simplification 78.3%

    \[\leadsto \frac{\frac{1}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{6} + {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)} - \frac{{\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{9}}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{6} + {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)} \]
12. Add Preprocessing

Alternative 2: 79.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\left(-x\right) \cdot x}\\ t_1 := 0.3275911 \cdot \left|x\right|\\ t_2 := {\left(1 + t\_1\right)}^{-1}\\ t_3 := 1.421413741 + t\_2 \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\\ t_4 := \left(t\_2 \cdot \left(0.254829592 + t\_2 \cdot \left(-0.284496736 + t\_2 \cdot t\_3\right)\right)\right) \cdot t\_0\\ t_5 := {t\_4}^{3}\\ \frac{\frac{1 - {t\_5}^{3}}{1 + \mathsf{fma}\left(t\_5, t\_5, t\_5\right)}}{1 + \mathsf{fma}\left(t\_4, t\_4, \left(t\_2 \cdot \left(0.254829592 + t\_2 \cdot \left(-0.284496736 + e^{\mathsf{log1p}\left(t\_1\right) \cdot -1} \cdot t\_3\right)\right)\right) \cdot t\_0\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (exp (* (- x) x)))
        (t_1 (* 0.3275911 (fabs x)))
        (t_2 (pow (+ 1.0 t_1) -1.0))
        (t_3
         (+
          1.421413741
          (*
           t_2
           (+
            -1.453152027
            (/
             1.061405429
             (/
              (- (* 0.10731592879921 (* x x)) 1.0)
              (- (* (fabs x) 0.3275911) 1.0)))))))
        (t_4
         (* (* t_2 (+ 0.254829592 (* t_2 (+ -0.284496736 (* t_2 t_3))))) t_0))
        (t_5 (pow t_4 3.0)))
   (/
    (/ (- 1.0 (pow t_5 3.0)) (+ 1.0 (fma t_5 t_5 t_5)))
    (+
     1.0
     (fma
      t_4
      t_4
      (*
       (*
        t_2
        (+
         0.254829592
         (* t_2 (+ -0.284496736 (* (exp (* (log1p t_1) -1.0)) t_3)))))
       t_0))))))

C

double code(double x) {
	double t_0 = exp((-x * x));
	double t_1 = 0.3275911 * fabs(x);
	double t_2 = pow((1.0 + t_1), -1.0);
	double t_3 = 1.421413741 + (t_2 * (-1.453152027 + (1.061405429 / (((0.10731592879921 * (x * x)) - 1.0) / ((fabs(x) * 0.3275911) - 1.0)))));
	double t_4 = (t_2 * (0.254829592 + (t_2 * (-0.284496736 + (t_2 * t_3))))) * t_0;
	double t_5 = pow(t_4, 3.0);
	return ((1.0 - pow(t_5, 3.0)) / (1.0 + fma(t_5, t_5, t_5))) / (1.0 + fma(t_4, t_4, ((t_2 * (0.254829592 + (t_2 * (-0.284496736 + (exp((log1p(t_1) * -1.0)) * t_3))))) * t_0)));
}

Julia

function code(x)
	t_0 = exp(Float64(Float64(-x) * x))
	t_1 = Float64(0.3275911 * abs(x))
	t_2 = Float64(1.0 + t_1) ^ -1.0
	t_3 = Float64(1.421413741 + Float64(t_2 * Float64(-1.453152027 + Float64(1.061405429 / Float64(Float64(Float64(0.10731592879921 * Float64(x * x)) - 1.0) / Float64(Float64(abs(x) * 0.3275911) - 1.0))))))
	t_4 = Float64(Float64(t_2 * Float64(0.254829592 + Float64(t_2 * Float64(-0.284496736 + Float64(t_2 * t_3))))) * t_0)
	t_5 = t_4 ^ 3.0
	return Float64(Float64(Float64(1.0 - (t_5 ^ 3.0)) / Float64(1.0 + fma(t_5, t_5, t_5))) / Float64(1.0 + fma(t_4, t_4, Float64(Float64(t_2 * Float64(0.254829592 + Float64(t_2 * Float64(-0.284496736 + Float64(exp(Float64(log1p(t_1) * -1.0)) * t_3))))) * t_0))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(1.0 + t$95$1), $MachinePrecision], -1.0], $MachinePrecision]}, Block[{t$95$3 = N[(1.421413741 + N[(t$95$2 * N[(-1.453152027 + N[(1.061405429 / N[(N[(N[(0.10731592879921 * N[(x * x), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] / N[(N[(N[Abs[x], $MachinePrecision] * 0.3275911), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 * N[(0.254829592 + N[(t$95$2 * N[(-0.284496736 + N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[Power[t$95$4, 3.0], $MachinePrecision]}, N[(N[(N[(1.0 - N[Power[t$95$5, 3.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$5 * t$95$5 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t$95$4 * t$95$4 + N[(N[(t$95$2 * N[(0.254829592 + N[(t$95$2 * N[(-0.284496736 + N[(N[Exp[N[(N[Log[1 + t$95$1], $MachinePrecision] * -1.0), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 76.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fabs.f64 N/A

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

   4. +-commutative N/A

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

   5. flip-+ N/A

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

   6. lower-/.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower--.f64 N/A

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

   9. lift-fabs.f64 N/A

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

   10. lift-fabs.f64 N/A

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

   11. swap-sqr N/A

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

   12. lift-*.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. metadata-eval N/A

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

   15. lift-*.f64 N/A

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

   16. lift-fabs.f64 N/A

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

   17. lift-fabs.f64 N/A

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

   18. sqr-abs N/A

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

   19. lower-*.f64 N/A

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

   20. lower--.f64 N/A

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

4. Applied rewrites 76.9%

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

6. Applied rewrites 77.0%

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

8. Applied rewrites 77.1%

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

   1. lift-pow.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + \color{blue}{{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1}} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   2. lift-+.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\color{blue}{\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \color{blue}{\frac{3275911}{10000000} \cdot \left|x\right|}\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   4. lift-fabs.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \color{blue}{\left|x\right|}\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   5. pow-to-exp N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + \color{blue}{e^{\log \left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot -1}} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   6. lower-exp.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + \color{blue}{e^{\log \left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot -1}} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   7. lower-*.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + e^{\color{blue}{\log \left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right) \cdot -1}} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   8. lower-log1p.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + e^{\color{blue}{\mathsf{log1p}\left(\frac{3275911}{10000000} \cdot \left|x\right|\right)} \cdot -1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   9. lift-fabs.f64 N/A

      \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{31853699}{125000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-8890523}{31250000} + e^{\mathsf{log1p}\left(\frac{3275911}{10000000} \cdot \color{blue}{\left|x\right|}\right) \cdot -1} \cdot \left(\frac{1421413741}{1000000000} + {\left(1 + \frac{3275911}{10000000} \cdot \left|x\right|\right)}^{-1} \cdot \left(\frac{-1453152027}{1000000000} + \frac{\frac{1061405429}{1000000000}}{\frac{\frac{10731592879921}{100000000000000} \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot \frac{3275911}{10000000} - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

   10. lift-*.f64 77.1

       \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + e^{\mathsf{log1p}\left(\color{blue}{0.3275911 \cdot \left|x\right|}\right) \cdot -1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

10. Applied rewrites 77.1%

    \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, 1 \cdot {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, 1 \cdot \left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + \color{blue}{e^{\mathsf{log1p}\left(0.3275911 \cdot \left|x\right|\right) \cdot -1}} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)} \]

11. Final simplification 77.1%

    \[\leadsto \frac{\frac{1 - {\left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}^{3}}{1 + \mathsf{fma}\left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}, {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \mathsf{fma}\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}, \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + e^{\mathsf{log1p}\left(0.3275911 \cdot \left|x\right|\right) \cdot -1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)} \]
12. Add Preprocessing

Alternative 3: 79.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fabs.f64 N/A

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

   4. +-commutative N/A

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

   5. flip-+ N/A

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

   6. lower-/.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower--.f64 N/A

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

   9. lift-fabs.f64 N/A

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

   10. lift-fabs.f64 N/A

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

   11. swap-sqr N/A

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

   12. lift-*.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. metadata-eval N/A

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

   15. lift-*.f64 N/A

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

   16. lift-fabs.f64 N/A

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

   17. lift-fabs.f64 N/A

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

   18. sqr-abs N/A

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

   19. lower-*.f64 N/A

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

   20. lower--.f64 N/A

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

4. Applied rewrites 76.9%

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

6. Applied rewrites 77.0%

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

8. Applied rewrites 77.1%

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

9. Final simplification 77.1%

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

Alternative 4: 79.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1}\\ t_1 := \left(t\_0 \cdot \left(0.254829592 + t\_0 \cdot \left(-0.284496736 + t\_0 \cdot \left(1.421413741 + t\_0 \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\\ \frac{\frac{1 - {t\_1}^{9}}{1 + \left({t\_1}^{6} + {t\_1}^{3}\right)}}{1 + \left({t\_1}^{2} + t\_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (* 0.3275911 (fabs x))) -1.0))
        (t_1
         (*
          (*
           t_0
           (+
            0.254829592
            (*
             t_0
             (+
              -0.284496736
              (*
               t_0
               (+
                1.421413741
                (*
                 t_0
                 (+
                  -1.453152027
                  (/
                   1.061405429
                   (/
                    (- (* 0.10731592879921 (* x x)) 1.0)
                    (- (* (fabs x) 0.3275911) 1.0)))))))))))
          (exp (* (- x) x)))))
   (/
    (/ (- 1.0 (pow t_1 9.0)) (+ 1.0 (+ (pow t_1 6.0) (pow t_1 3.0))))
    (+ 1.0 (+ (pow t_1 2.0) t_1)))))

C

double code(double x) {
	double t_0 = pow((1.0 + (0.3275911 * fabs(x))), -1.0);
	double t_1 = (t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (1.061405429 / (((0.10731592879921 * (x * x)) - 1.0) / ((fabs(x) * 0.3275911) - 1.0))))))))))) * exp((-x * x));
	return ((1.0 - pow(t_1, 9.0)) / (1.0 + (pow(t_1, 6.0) + pow(t_1, 3.0)))) / (1.0 + (pow(t_1, 2.0) + t_1));
}

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
    real(8) :: t_1
    t_0 = (1.0d0 + (0.3275911d0 * abs(x))) ** (-1.0d0)
    t_1 = (t_0 * (0.254829592d0 + (t_0 * ((-0.284496736d0) + (t_0 * (1.421413741d0 + (t_0 * ((-1.453152027d0) + (1.061405429d0 / (((0.10731592879921d0 * (x * x)) - 1.0d0) / ((abs(x) * 0.3275911d0) - 1.0d0))))))))))) * exp((-x * x))
    code = ((1.0d0 - (t_1 ** 9.0d0)) / (1.0d0 + ((t_1 ** 6.0d0) + (t_1 ** 3.0d0)))) / (1.0d0 + ((t_1 ** 2.0d0) + t_1))
end function

Java

public static double code(double x) {
	double t_0 = Math.pow((1.0 + (0.3275911 * Math.abs(x))), -1.0);
	double t_1 = (t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (1.061405429 / (((0.10731592879921 * (x * x)) - 1.0) / ((Math.abs(x) * 0.3275911) - 1.0))))))))))) * Math.exp((-x * x));
	return ((1.0 - Math.pow(t_1, 9.0)) / (1.0 + (Math.pow(t_1, 6.0) + Math.pow(t_1, 3.0)))) / (1.0 + (Math.pow(t_1, 2.0) + t_1));
}

Python

def code(x):
	t_0 = math.pow((1.0 + (0.3275911 * math.fabs(x))), -1.0)
	t_1 = (t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (1.061405429 / (((0.10731592879921 * (x * x)) - 1.0) / ((math.fabs(x) * 0.3275911) - 1.0))))))))))) * math.exp((-x * x))
	return ((1.0 - math.pow(t_1, 9.0)) / (1.0 + (math.pow(t_1, 6.0) + math.pow(t_1, 3.0)))) / (1.0 + (math.pow(t_1, 2.0) + t_1))

Julia

function code(x)
	t_0 = Float64(1.0 + Float64(0.3275911 * abs(x))) ^ -1.0
	t_1 = 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(1.061405429 / Float64(Float64(Float64(0.10731592879921 * Float64(x * x)) - 1.0) / Float64(Float64(abs(x) * 0.3275911) - 1.0))))))))))) * exp(Float64(Float64(-x) * x)))
	return Float64(Float64(Float64(1.0 - (t_1 ^ 9.0)) / Float64(1.0 + Float64((t_1 ^ 6.0) + (t_1 ^ 3.0)))) / Float64(1.0 + Float64((t_1 ^ 2.0) + t_1)))
end

MATLAB

function tmp = code(x)
	t_0 = (1.0 + (0.3275911 * abs(x))) ^ -1.0;
	t_1 = (t_0 * (0.254829592 + (t_0 * (-0.284496736 + (t_0 * (1.421413741 + (t_0 * (-1.453152027 + (1.061405429 / (((0.10731592879921 * (x * x)) - 1.0) / ((abs(x) * 0.3275911) - 1.0))))))))))) * exp((-x * x));
	tmp = ((1.0 - (t_1 ^ 9.0)) / (1.0 + ((t_1 ^ 6.0) + (t_1 ^ 3.0)))) / (1.0 + ((t_1 ^ 2.0) + t_1));
end

Wolfram

code[x_] := Block[{t$95$0 = N[Power[N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]}, Block[{t$95$1 = 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[(1.061405429 / N[(N[(N[(0.10731592879921 * N[(x * x), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] / N[(N[(N[Abs[x], $MachinePrecision] * 0.3275911), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1.0 - N[Power[t$95$1, 9.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$1, 6.0], $MachinePrecision] + N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[Power[t$95$1, 2.0], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 76.8%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-fabs.f64 N/A

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

   4. +-commutative N/A

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

   5. flip-+ N/A

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

   6. lower-/.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower--.f64 N/A

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

   9. lift-fabs.f64 N/A

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

   10. lift-fabs.f64 N/A

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

   11. swap-sqr N/A

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

   12. lift-*.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. metadata-eval N/A

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

   15. lift-*.f64 N/A

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

   16. lift-fabs.f64 N/A

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

   17. lift-fabs.f64 N/A

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

   18. sqr-abs N/A

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

   19. lower-*.f64 N/A

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

   20. lower--.f64 N/A

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

4. Applied rewrites 76.9%

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

6. Applied rewrites 77.0%

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

8. Applied rewrites 77.1%

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

10. Applied rewrites 77.1%

    \[\leadsto \color{blue}{\frac{\frac{1 - {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{9}}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{6} + 1 \cdot {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{2} + 1 \cdot \left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)\right)}} \]

11. Final simplification 77.1%

    \[\leadsto \frac{\frac{1 - {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{9}}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{6} + {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{3}\right)}}{1 + \left({\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{2} + \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-0.284496736 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(1.421413741 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(-1.453152027 + \frac{1.061405429}{\frac{0.10731592879921 \cdot \left(x \cdot x\right) - 1}{\left|x\right| \cdot 0.3275911 - 1}}\right)\right)\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)} \]
12. Add Preprocessing

Alternative 5: 79.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\left(-x\right) \cdot x}\\ t_1 := {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1}\\ t_2 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_3 := 1 - 0.10731592879921 \cdot \left(x \cdot x\right)\\ t_4 := 1 - \left|x\right| \cdot 0.3275911\\ t_5 := \left(t\_1 \cdot \left(0.254829592 + t\_1 \cdot \mathsf{fma}\left(\frac{\frac{\frac{1.061405429}{t\_2} - 1.453152027}{t\_2} - -1.421413741}{t\_3}, t\_4, -0.284496736\right)\right)\right) \cdot t\_0\\ \frac{1 - t\_5 \cdot \left(\left(t\_1 \cdot \left(0.254829592 + t\_1 \cdot \mathsf{fma}\left(\frac{\frac{1.061405429 \cdot t\_1 - 1.453152027}{t\_2} - -1.421413741}{t\_3}, t\_4, -0.284496736\right)\right)\right) \cdot t\_0\right)}{1 + t\_5} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (exp (* (- x) x)))
        (t_1 (pow (+ 1.0 (* 0.3275911 (fabs x))) -1.0))
        (t_2 (fma (fabs x) 0.3275911 1.0))
        (t_3 (- 1.0 (* 0.10731592879921 (* x x))))
        (t_4 (- 1.0 (* (fabs x) 0.3275911)))
        (t_5
         (*
          (*
           t_1
           (+
            0.254829592
            (*
             t_1
             (fma
              (/
               (- (/ (- (/ 1.061405429 t_2) 1.453152027) t_2) -1.421413741)
               t_3)
              t_4
              -0.284496736))))
          t_0)))
   (/
    (-
     1.0
     (*
      t_5
      (*
       (*
        t_1
        (+
         0.254829592
         (*
          t_1
          (fma
           (/ (- (/ (- (* 1.061405429 t_1) 1.453152027) t_2) -1.421413741) t_3)
           t_4
           -0.284496736))))
       t_0)))
    (+ 1.0 t_5))))

C

double code(double x) {
	double t_0 = exp((-x * x));
	double t_1 = pow((1.0 + (0.3275911 * fabs(x))), -1.0);
	double t_2 = fma(fabs(x), 0.3275911, 1.0);
	double t_3 = 1.0 - (0.10731592879921 * (x * x));
	double t_4 = 1.0 - (fabs(x) * 0.3275911);
	double t_5 = (t_1 * (0.254829592 + (t_1 * fma((((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_3), t_4, -0.284496736)))) * t_0;
	return (1.0 - (t_5 * ((t_1 * (0.254829592 + (t_1 * fma((((((1.061405429 * t_1) - 1.453152027) / t_2) - -1.421413741) / t_3), t_4, -0.284496736)))) * t_0))) / (1.0 + t_5);
}

Julia

function code(x)
	t_0 = exp(Float64(Float64(-x) * x))
	t_1 = Float64(1.0 + Float64(0.3275911 * abs(x))) ^ -1.0
	t_2 = fma(abs(x), 0.3275911, 1.0)
	t_3 = Float64(1.0 - Float64(0.10731592879921 * Float64(x * x)))
	t_4 = Float64(1.0 - Float64(abs(x) * 0.3275911))
	t_5 = Float64(Float64(t_1 * Float64(0.254829592 + Float64(t_1 * fma(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_3), t_4, -0.284496736)))) * t_0)
	return Float64(Float64(1.0 - Float64(t_5 * Float64(Float64(t_1 * Float64(0.254829592 + Float64(t_1 * fma(Float64(Float64(Float64(Float64(Float64(1.061405429 * t_1) - 1.453152027) / t_2) - -1.421413741) / t_3), t_4, -0.284496736)))) * t_0))) / Float64(1.0 + t_5))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]}, Block[{t$95$2 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 - N[(0.10731592879921 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(1.0 - N[(N[Abs[x], $MachinePrecision] * 0.3275911), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$1 * N[(0.254829592 + N[(t$95$1 * N[(N[(N[(N[(N[(N[(1.061405429 / t$95$2), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$2), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] * t$95$4 + -0.284496736), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]}, N[(N[(1.0 - N[(t$95$5 * N[(N[(t$95$1 * N[(0.254829592 + N[(t$95$1 * N[(N[(N[(N[(N[(N[(1.061405429 * t$95$1), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$2), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$3), $MachinePrecision] * t$95$4 + -0.284496736), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

6. Applied rewrites 76.9%

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

7. Taylor expanded in x around 0

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

9. Applied rewrites 77.0%

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

Alternative 6: 79.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1}\\ t_1 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_2 := \left(t\_0 \cdot \left(0.254829592 + t\_0 \cdot \mathsf{fma}\left(\frac{\frac{\frac{1.061405429}{t\_1} - 1.453152027}{t\_1} - -1.421413741}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}, 1 - \left|x\right| \cdot 0.3275911, -0.284496736\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\\ \frac{1 - {t\_2}^{2}}{1 + t\_2} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (* 0.3275911 (fabs x))) -1.0))
        (t_1 (fma (fabs x) 0.3275911 1.0))
        (t_2
         (*
          (*
           t_0
           (+
            0.254829592
            (*
             t_0
             (fma
              (/
               (- (/ (- (/ 1.061405429 t_1) 1.453152027) t_1) -1.421413741)
               (- 1.0 (* 0.10731592879921 (* x x))))
              (- 1.0 (* (fabs x) 0.3275911))
              -0.284496736))))
          (exp (* (- x) x)))))
   (/ (- 1.0 (pow t_2 2.0)) (+ 1.0 t_2))))

C

double code(double x) {
	double t_0 = pow((1.0 + (0.3275911 * fabs(x))), -1.0);
	double t_1 = fma(fabs(x), 0.3275911, 1.0);
	double t_2 = (t_0 * (0.254829592 + (t_0 * fma((((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / (1.0 - (0.10731592879921 * (x * x)))), (1.0 - (fabs(x) * 0.3275911)), -0.284496736)))) * exp((-x * x));
	return (1.0 - pow(t_2, 2.0)) / (1.0 + t_2);
}

Julia

function code(x)
	t_0 = Float64(1.0 + Float64(0.3275911 * abs(x))) ^ -1.0
	t_1 = fma(abs(x), 0.3275911, 1.0)
	t_2 = Float64(Float64(t_0 * Float64(0.254829592 + Float64(t_0 * fma(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / Float64(1.0 - Float64(0.10731592879921 * Float64(x * x)))), Float64(1.0 - Float64(abs(x) * 0.3275911)), -0.284496736)))) * exp(Float64(Float64(-x) * x)))
	return Float64(Float64(1.0 - (t_2 ^ 2.0)) / Float64(1.0 + t_2))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Power[N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$0 * N[(0.254829592 + N[(t$95$0 * N[(N[(N[(N[(N[(N[(1.061405429 / t$95$1), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$1), $MachinePrecision] - -1.421413741), $MachinePrecision] / N[(1.0 - N[(0.10731592879921 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 - N[(N[Abs[x], $MachinePrecision] * 0.3275911), $MachinePrecision]), $MachinePrecision] + -0.284496736), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(N[(1.0 - N[Power[t$95$2, 2.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

6. Applied rewrites 76.9%

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

8. Applied rewrites 76.9%

   \[\leadsto \color{blue}{\frac{1 - {\left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \mathsf{fma}\left(\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}, 1 - \left|x\right| \cdot 0.3275911, -0.284496736\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}\right)}^{2}}{1 + \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \left(0.254829592 + {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{-1} \cdot \mathsf{fma}\left(\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{1 - 0.10731592879921 \cdot \left(x \cdot x\right)}, 1 - \left|x\right| \cdot 0.3275911, -0.284496736\right)\right)\right) \cdot e^{\left(-x\right) \cdot x}}} \]
9. Add Preprocessing

Alternative 7: 79.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

   1. lift-fabs.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. flip-+ N/A

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

   4. lift-fabs.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-fabs.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. metadata-eval N/A

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

   10. lift--.f64 N/A

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

   11. lift-fabs.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift--.f64 N/A

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

   14. lift-/.f64 76.9

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

6. Applied rewrites 76.9%

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

Alternative 8: 79.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

   1. lift-fabs.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. flip-+ N/A

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

   4. lift-fabs.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-fabs.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. metadata-eval N/A

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

   10. lift--.f64 N/A

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

   11. lift-fabs.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. lift--.f64 N/A

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

   14. lift-/.f64 76.9

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

6. Applied rewrites 76.9%

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

Alternative 9: 79.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 76.9

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

6. Applied rewrites 76.9%

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

Alternative 10: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

5. Final simplification 76.9%

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

Alternative 11: 79.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 76.9

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

6. Applied rewrites 76.9%

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

Alternative 12: 79.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

Alternative 13: 55.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := 1 + 0.3275911 \cdot \left|x\right|\\ \mathbf{if}\;x \leq 1.3:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\left(\frac{\frac{1.061405429}{t\_0}}{t\_0} - \frac{1.453152027}{t\_0}\right) - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{e^{\left(-x\right) \cdot x} \cdot \left(0.254829592 - \frac{0.284496736}{t\_1}\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (+ 1.0 (* 0.3275911 (fabs x)))))
   (if (<= x 1.3)
     (fma
      (/
       (+
        (/
         (+
          (/
           (- (- (/ (/ 1.061405429 t_0) t_0) (/ 1.453152027 t_0)) -1.421413741)
           t_0)
          -0.284496736)
         t_0)
        0.254829592)
       (fma -0.3275911 (fabs x) -1.0))
      (+
       1.0
       (*
        (* x x)
        (- (* (* x x) (+ 0.5 (* -0.16666666666666666 (* x x)))) 1.0)))
      1.0)
     (-
      1.0
      (/ (* (exp (* (- x) x)) (- 0.254829592 (/ 0.284496736 t_1))) t_1)))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = 1.0 + (0.3275911 * fabs(x));
	double tmp;
	if (x <= 1.3) {
		tmp = fma((((((((((1.061405429 / t_0) / t_0) - (1.453152027 / t_0)) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, fabs(x), -1.0)), (1.0 + ((x * x) * (((x * x) * (0.5 + (-0.16666666666666666 * (x * x)))) - 1.0))), 1.0);
	} else {
		tmp = 1.0 - ((exp((-x * x)) * (0.254829592 - (0.284496736 / t_1))) / t_1);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(1.0 + Float64(0.3275911 * abs(x)))
	tmp = 0.0
	if (x <= 1.3)
		tmp = fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) / t_0) - Float64(1.453152027 / t_0)) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, abs(x), -1.0)), Float64(1.0 + Float64(Float64(x * x) * Float64(Float64(Float64(x * x) * Float64(0.5 + Float64(-0.16666666666666666 * Float64(x * x)))) - 1.0))), 1.0);
	else
		tmp = Float64(1.0 - Float64(Float64(exp(Float64(Float64(-x) * x)) * Float64(0.254829592 - Float64(0.284496736 / t_1))) / t_1));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.3], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision] - N[(1.453152027 / t$95$0), $MachinePrecision]), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(0.254829592 - N[(0.284496736 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.30000000000000004

   1. Initial program 71.2%

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

   4. Applied rewrites 71.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 71.3

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

   6. Applied rewrites 71.3%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 41.1%

      \[\leadsto \mathsf{fma}\left(\frac{\frac{\frac{\left(\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - \frac{1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)}\right) - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, \color{blue}{1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right)}, 1\right) \]

   if 1.30000000000000004 < x

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 100.0%

      \[\leadsto 1 - \color{blue}{\frac{e^{\left(-x\right) \cdot x} \cdot \left(0.254829592 - \frac{0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right)}{1 + 0.3275911 \cdot \left|x\right|}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 55.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ t_1 := 1 + 0.3275911 \cdot \left|x\right|\\ \mathbf{if}\;x \leq 1.3:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{e^{\left(-x\right) \cdot x} \cdot \left(0.254829592 - \frac{0.284496736}{t\_1}\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0))
        (t_1 (+ 1.0 (* 0.3275911 (fabs x)))))
   (if (<= x 1.3)
     (fma
      (/
       (+
        (/
         (+
          (/ (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741) t_0)
          -0.284496736)
         t_0)
        0.254829592)
       (fma -0.3275911 (fabs x) -1.0))
      (+
       1.0
       (*
        (* x x)
        (- (* (* x x) (+ 0.5 (* -0.16666666666666666 (* x x)))) 1.0)))
      1.0)
     (-
      1.0
      (/ (* (exp (* (- x) x)) (- 0.254829592 (/ 0.284496736 t_1))) t_1)))))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double t_1 = 1.0 + (0.3275911 * fabs(x));
	double tmp;
	if (x <= 1.3) {
		tmp = fma((((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, fabs(x), -1.0)), (1.0 + ((x * x) * (((x * x) * (0.5 + (-0.16666666666666666 * (x * x)))) - 1.0))), 1.0);
	} else {
		tmp = 1.0 - ((exp((-x * x)) * (0.254829592 - (0.284496736 / t_1))) / t_1);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	t_1 = Float64(1.0 + Float64(0.3275911 * abs(x)))
	tmp = 0.0
	if (x <= 1.3)
		tmp = fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, abs(x), -1.0)), Float64(1.0 + Float64(Float64(x * x) * Float64(Float64(Float64(x * x) * Float64(0.5 + Float64(-0.16666666666666666 * Float64(x * x)))) - 1.0))), 1.0);
	else
		tmp = Float64(1.0 - Float64(Float64(exp(Float64(Float64(-x) * x)) * Float64(0.254829592 - Float64(0.284496736 / t_1))) / t_1));
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(0.3275911 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.3], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(0.254829592 - N[(0.284496736 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.30000000000000004

   1. Initial program 71.2%

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 41.1%

      \[\leadsto \mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, \color{blue}{1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right)}, 1\right) \]

   if 1.30000000000000004 < x

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 100.0%

      \[\leadsto 1 - \color{blue}{\frac{e^{\left(-x\right) \cdot x} \cdot \left(0.254829592 - \frac{0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right)}{1 + 0.3275911 \cdot \left|x\right|}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.3:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{e^{\left(-x\right) \cdot x} \cdot \left(0.254829592 - \frac{0.284496736}{1 + 0.3275911 \cdot \left|x\right|}\right)}{1 + 0.3275911 \cdot \left|x\right|}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ \mathbf{if}\;x \leq 1.3:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (if (<= x 1.3)
     (fma
      (/
       (+
        (/
         (+
          (/ (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741) t_0)
          -0.284496736)
         t_0)
        0.254829592)
       (fma -0.3275911 (fabs x) -1.0))
      (+
       1.0
       (*
        (* x x)
        (- (* (* x x) (+ 0.5 (* -0.16666666666666666 (* x x)))) 1.0)))
      1.0)
     1.0)))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double tmp;
	if (x <= 1.3) {
		tmp = fma((((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, fabs(x), -1.0)), (1.0 + ((x * x) * (((x * x) * (0.5 + (-0.16666666666666666 * (x * x)))) - 1.0))), 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	tmp = 0.0
	if (x <= 1.3)
		tmp = fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, abs(x), -1.0)), Float64(1.0 + Float64(Float64(x * x) * Float64(Float64(Float64(x * x) * Float64(0.5 + Float64(-0.16666666666666666 * Float64(x * x)))) - 1.0))), 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, If[LessEqual[x, 1.3], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < 1.30000000000000004

   1. Initial program 71.2%

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 41.1%

      \[\leadsto \mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, \color{blue}{1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right)}, 1\right) \]

   if 1.30000000000000004 < x

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.3:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot \left(0.5 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ \mathbf{if}\;x \leq 1.15:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(0.5 \cdot \left(x \cdot x\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (if (<= x 1.15)
     (fma
      (/
       (+
        (/
         (+
          (/ (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741) t_0)
          -0.284496736)
         t_0)
        0.254829592)
       (fma -0.3275911 (fabs x) -1.0))
      (+ 1.0 (* (* x x) (- (* 0.5 (* x x)) 1.0)))
      1.0)
     1.0)))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double tmp;
	if (x <= 1.15) {
		tmp = fma((((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, fabs(x), -1.0)), (1.0 + ((x * x) * ((0.5 * (x * x)) - 1.0))), 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	tmp = 0.0
	if (x <= 1.15)
		tmp = fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, abs(x), -1.0)), Float64(1.0 + Float64(Float64(x * x) * Float64(Float64(0.5 * Float64(x * x)) - 1.0))), 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, If[LessEqual[x, 1.15], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < 1.1499999999999999

   1. Initial program 71.2%

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 40.0%

      \[\leadsto \mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, \color{blue}{1 + \left(x \cdot x\right) \cdot \left(0.5 \cdot \left(x \cdot x\right) - 1\right)}, 1\right) \]

   if 1.1499999999999999 < x

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.15:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 + \left(x \cdot x\right) \cdot \left(0.5 \cdot \left(x \cdot x\right) - 1\right), 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.6% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	tmp = 0.0
	if (x <= 1.0)
		tmp = fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, abs(x), -1.0)), Float64(1.0 - Float64(x * x)), 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 71.2%

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 41.4%

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

   if 1 < x

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1 - x \cdot x, 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 78.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)\\ \mathbf{if}\;x \leq 0.82:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{t\_0} - 1.453152027}{t\_0} - -1.421413741}{t\_0} + -0.284496736}{t\_0} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1, 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (fma (fabs x) 0.3275911 1.0)))
   (if (<= x 0.82)
     (fma
      (/
       (+
        (/
         (+
          (/ (- (/ (- (/ 1.061405429 t_0) 1.453152027) t_0) -1.421413741) t_0)
          -0.284496736)
         t_0)
        0.254829592)
       (fma -0.3275911 (fabs x) -1.0))
      1.0
      1.0)
     1.0)))

C

double code(double x) {
	double t_0 = fma(fabs(x), 0.3275911, 1.0);
	double tmp;
	if (x <= 0.82) {
		tmp = fma((((((((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, fabs(x), -1.0)), 1.0, 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x)
	t_0 = fma(abs(x), 0.3275911, 1.0)
	tmp = 0.0
	if (x <= 0.82)
		tmp = fma(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_0) + -0.284496736) / t_0) + 0.254829592) / fma(-0.3275911, abs(x), -1.0)), 1.0, 1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 0.3275911 + 1.0), $MachinePrecision]}, If[LessEqual[x, 0.82], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1.061405429 / t$95$0), $MachinePrecision] - 1.453152027), $MachinePrecision] / t$95$0), $MachinePrecision] - -1.421413741), $MachinePrecision] / t$95$0), $MachinePrecision] + -0.284496736), $MachinePrecision] / t$95$0), $MachinePrecision] + 0.254829592), $MachinePrecision] / N[(-0.3275911 * N[Abs[x], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] * 1.0 + 1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < 0.819999999999999951

   1. Initial program 71.2%

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 68.6%

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

   if 0.819999999999999951 < x

   1. Initial program 100.0%

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.82:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{\frac{\frac{\frac{1.061405429}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - 1.453152027}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} - -1.421413741}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + -0.284496736}{\mathsf{fma}\left(\left|x\right|, 0.3275911, 1\right)} + 0.254829592}{\mathsf{fma}\left(-0.3275911, \left|x\right|, -1\right)}, 1, 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 55.5% accurate, 262.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

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
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 76.8%

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

4. Applied rewrites 76.9%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
6. Step-by-step derivation

7. Applied rewrites 50.6%

   \[\leadsto \color{blue}{1} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025025 
(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)))))))