Jmat.Real.dawson

Percentage Accurate: 53.9% → 56.5%

Time: 17.6s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ t_1 := t\_0 \cdot \left(x \cdot x\right)\\ t_2 := t\_1 \cdot \left(x \cdot x\right)\\ t_3 := t\_2 \cdot \left(x \cdot x\right)\\ \frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot t\_0\right) + 0.0072644182 \cdot t\_1\right) + 0.0005064034 \cdot t\_2\right) + 0.0001789971 \cdot t\_3}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot t\_0\right) + 0.0694555761 \cdot t\_1\right) + 0.0140005442 \cdot t\_2\right) + 0.0008327945 \cdot t\_3\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(t\_3 \cdot \left(x \cdot x\right)\right)} \cdot x \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (* x x) (* x x)))
        (t_1 (* t_0 (* x x)))
        (t_2 (* t_1 (* x x)))
        (t_3 (* t_2 (* x x))))
   (*
    (/
     (+
      (+
       (+
        (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 t_0))
        (* 0.0072644182 t_1))
       (* 0.0005064034 t_2))
      (* 0.0001789971 t_3))
     (+
      (+
       (+
        (+
         (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 t_0))
         (* 0.0694555761 t_1))
        (* 0.0140005442 t_2))
       (* 0.0008327945 t_3))
      (* (* 2.0 0.0001789971) (* t_3 (* x x)))))
    x)))

C

double code(double x) {
	double t_0 = (x * x) * (x * x);
	double t_1 = t_0 * (x * x);
	double t_2 = t_1 * (x * x);
	double t_3 = t_2 * (x * x);
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * 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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    t_0 = (x * x) * (x * x)
    t_1 = t_0 * (x * x)
    t_2 = t_1 * (x * x)
    t_3 = t_2 * (x * x)
    code = ((((((1.0d0 + (0.1049934947d0 * (x * x))) + (0.0424060604d0 * t_0)) + (0.0072644182d0 * t_1)) + (0.0005064034d0 * t_2)) + (0.0001789971d0 * t_3)) / ((((((1.0d0 + (0.7715471019d0 * (x * x))) + (0.2909738639d0 * t_0)) + (0.0694555761d0 * t_1)) + (0.0140005442d0 * t_2)) + (0.0008327945d0 * t_3)) + ((2.0d0 * 0.0001789971d0) * (t_3 * (x * x))))) * x
end function

Java

public static double code(double x) {
	double t_0 = (x * x) * (x * x);
	double t_1 = t_0 * (x * x);
	double t_2 = t_1 * (x * x);
	double t_3 = t_2 * (x * x);
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * x;
}

Python

def code(x):
	t_0 = (x * x) * (x * x)
	t_1 = t_0 * (x * x)
	t_2 = t_1 * (x * x)
	t_3 = t_2 * (x * x)
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * x

Julia

function code(x)
	t_0 = Float64(Float64(x * x) * Float64(x * x))
	t_1 = Float64(t_0 * Float64(x * x))
	t_2 = Float64(t_1 * Float64(x * x))
	t_3 = Float64(t_2 * Float64(x * x))
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.1049934947 * Float64(x * x))) + Float64(0.0424060604 * t_0)) + Float64(0.0072644182 * t_1)) + Float64(0.0005064034 * t_2)) + Float64(0.0001789971 * t_3)) / Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.7715471019 * Float64(x * x))) + Float64(0.2909738639 * t_0)) + Float64(0.0694555761 * t_1)) + Float64(0.0140005442 * t_2)) + Float64(0.0008327945 * t_3)) + Float64(Float64(2.0 * 0.0001789971) * Float64(t_3 * Float64(x * x))))) * x)
end

MATLAB

function tmp = code(x)
	t_0 = (x * x) * (x * x);
	t_1 = t_0 * (x * x);
	t_2 = t_1 * (x * x);
	t_3 = t_2 * (x * x);
	tmp = ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * x;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(N[(N[(N[(1.0 + N[(0.1049934947 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0424060604 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0072644182 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(0.0005064034 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0001789971 * t$95$3), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(1.0 + N[(0.7715471019 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.2909738639 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0694555761 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0008327945 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(t$95$3 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]

Initial Program: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot x\right) \cdot \left(x \cdot x\right)\\ t_1 := t\_0 \cdot \left(x \cdot x\right)\\ t_2 := t\_1 \cdot \left(x \cdot x\right)\\ t_3 := t\_2 \cdot \left(x \cdot x\right)\\ \frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot t\_0\right) + 0.0072644182 \cdot t\_1\right) + 0.0005064034 \cdot t\_2\right) + 0.0001789971 \cdot t\_3}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot t\_0\right) + 0.0694555761 \cdot t\_1\right) + 0.0140005442 \cdot t\_2\right) + 0.0008327945 \cdot t\_3\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(t\_3 \cdot \left(x \cdot x\right)\right)} \cdot x \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (* x x) (* x x)))
        (t_1 (* t_0 (* x x)))
        (t_2 (* t_1 (* x x)))
        (t_3 (* t_2 (* x x))))
   (*
    (/
     (+
      (+
       (+
        (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 t_0))
        (* 0.0072644182 t_1))
       (* 0.0005064034 t_2))
      (* 0.0001789971 t_3))
     (+
      (+
       (+
        (+
         (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 t_0))
         (* 0.0694555761 t_1))
        (* 0.0140005442 t_2))
       (* 0.0008327945 t_3))
      (* (* 2.0 0.0001789971) (* t_3 (* x x)))))
    x)))

C

double code(double x) {
	double t_0 = (x * x) * (x * x);
	double t_1 = t_0 * (x * x);
	double t_2 = t_1 * (x * x);
	double t_3 = t_2 * (x * x);
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * 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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    t_0 = (x * x) * (x * x)
    t_1 = t_0 * (x * x)
    t_2 = t_1 * (x * x)
    t_3 = t_2 * (x * x)
    code = ((((((1.0d0 + (0.1049934947d0 * (x * x))) + (0.0424060604d0 * t_0)) + (0.0072644182d0 * t_1)) + (0.0005064034d0 * t_2)) + (0.0001789971d0 * t_3)) / ((((((1.0d0 + (0.7715471019d0 * (x * x))) + (0.2909738639d0 * t_0)) + (0.0694555761d0 * t_1)) + (0.0140005442d0 * t_2)) + (0.0008327945d0 * t_3)) + ((2.0d0 * 0.0001789971d0) * (t_3 * (x * x))))) * x
end function

Java

public static double code(double x) {
	double t_0 = (x * x) * (x * x);
	double t_1 = t_0 * (x * x);
	double t_2 = t_1 * (x * x);
	double t_3 = t_2 * (x * x);
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * x;
}

Python

def code(x):
	t_0 = (x * x) * (x * x)
	t_1 = t_0 * (x * x)
	t_2 = t_1 * (x * x)
	t_3 = t_2 * (x * x)
	return ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * x

Julia

function code(x)
	t_0 = Float64(Float64(x * x) * Float64(x * x))
	t_1 = Float64(t_0 * Float64(x * x))
	t_2 = Float64(t_1 * Float64(x * x))
	t_3 = Float64(t_2 * Float64(x * x))
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.1049934947 * Float64(x * x))) + Float64(0.0424060604 * t_0)) + Float64(0.0072644182 * t_1)) + Float64(0.0005064034 * t_2)) + Float64(0.0001789971 * t_3)) / Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.7715471019 * Float64(x * x))) + Float64(0.2909738639 * t_0)) + Float64(0.0694555761 * t_1)) + Float64(0.0140005442 * t_2)) + Float64(0.0008327945 * t_3)) + Float64(Float64(2.0 * 0.0001789971) * Float64(t_3 * Float64(x * x))))) * x)
end

MATLAB

function tmp = code(x)
	t_0 = (x * x) * (x * x);
	t_1 = t_0 * (x * x);
	t_2 = t_1 * (x * x);
	t_3 = t_2 * (x * x);
	tmp = ((((((1.0 + (0.1049934947 * (x * x))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x * x))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x * x))))) * x;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(N[(N[(N[(1.0 + N[(0.1049934947 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0424060604 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0072644182 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(0.0005064034 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0001789971 * t$95$3), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(1.0 + N[(0.7715471019 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.2909738639 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0694555761 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0008327945 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(t$95$3 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]

Alternative 1: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := {\left(x\_m \cdot x\_m\right)}^{2}\\ t_1 := \left(x\_m \cdot x\_m\right) \cdot x\_m\\ t_2 := {t\_0}^{2}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x\_m, x\_m, 0.0005064034\right), t\_2, \mathsf{fma}\left(0.0072644182, t\_0, \mathsf{fma}\left(0.0424060604 \cdot x\_m, x\_m, 0.1049934947\right)\right) \cdot \left(x\_m \cdot x\_m\right)\right), x\_m, x\_m\right)}{\mathsf{fma}\left(x\_m \cdot x\_m, \mathsf{fma}\left(0.0008327945, t\_2, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x\_m \cdot x\_m\right)\right) \cdot \left(\left(t\_1 \cdot \left(x\_m \cdot x\_m\right)\right) \cdot t\_1\right)\right), \mathsf{fma}\left(0.0140005442, t\_2, \mathsf{fma}\left(0.0694555761, {t\_1}^{2}, \mathsf{fma}\left(x\_m \cdot x\_m, 0.7715471019 + \left(0.2909738639 \cdot x\_m\right) \cdot x\_m, 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x\_m \cdot x\_m, 0.0008327945\right), {\left(t\_0 \cdot x\_m\right)}^{2}, \mathsf{fma}\left(0.0140005442, \left(t\_1 \cdot t\_1\right) \cdot \left(x\_m \cdot x\_m\right), \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, t\_0, \mathsf{fma}\left(0.2909738639 \cdot x\_m, x\_m, 0.7715471019\right)\right), x\_m \cdot x\_m, 1\right)\right)\right)}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (pow (* x_m x_m) 2.0))
        (t_1 (* (* x_m x_m) x_m))
        (t_2 (pow t_0 2.0)))
   (*
    x_s
    (if (<= x_m 1e+26)
      (/
       (fma
        (fma
         (fma (* 0.0001789971 x_m) x_m 0.0005064034)
         t_2
         (*
          (fma 0.0072644182 t_0 (fma (* 0.0424060604 x_m) x_m 0.1049934947))
          (* x_m x_m)))
        x_m
        x_m)
       (fma
        (* x_m x_m)
        (fma
         0.0008327945
         t_2
         (* (* (* 2.0 0.0001789971) (* x_m x_m)) (* (* t_1 (* x_m x_m)) t_1)))
        (fma
         0.0140005442
         t_2
         (fma
          0.0694555761
          (pow t_1 2.0)
          (fma
           (* x_m x_m)
           (+ 0.7715471019 (* (* 0.2909738639 x_m) x_m))
           1.0)))))
      (/
       x_m
       (fma
        (fma (* 2.0 0.0001789971) (* x_m x_m) 0.0008327945)
        (pow (* t_0 x_m) 2.0)
        (fma
         0.0140005442
         (* (* t_1 t_1) (* x_m x_m))
         (fma
          (fma 0.0694555761 t_0 (fma (* 0.2909738639 x_m) x_m 0.7715471019))
          (* x_m x_m)
          1.0))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = pow((x_m * x_m), 2.0);
	double t_1 = (x_m * x_m) * x_m;
	double t_2 = pow(t_0, 2.0);
	double tmp;
	if (x_m <= 1e+26) {
		tmp = fma(fma(fma((0.0001789971 * x_m), x_m, 0.0005064034), t_2, (fma(0.0072644182, t_0, fma((0.0424060604 * x_m), x_m, 0.1049934947)) * (x_m * x_m))), x_m, x_m) / fma((x_m * x_m), fma(0.0008327945, t_2, (((2.0 * 0.0001789971) * (x_m * x_m)) * ((t_1 * (x_m * x_m)) * t_1))), fma(0.0140005442, t_2, fma(0.0694555761, pow(t_1, 2.0), fma((x_m * x_m), (0.7715471019 + ((0.2909738639 * x_m) * x_m)), 1.0))));
	} else {
		tmp = x_m / fma(fma((2.0 * 0.0001789971), (x_m * x_m), 0.0008327945), pow((t_0 * x_m), 2.0), fma(0.0140005442, ((t_1 * t_1) * (x_m * x_m)), fma(fma(0.0694555761, t_0, fma((0.2909738639 * x_m), x_m, 0.7715471019)), (x_m * x_m), 1.0)));
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(x_m * x_m) ^ 2.0
	t_1 = Float64(Float64(x_m * x_m) * x_m)
	t_2 = t_0 ^ 2.0
	tmp = 0.0
	if (x_m <= 1e+26)
		tmp = Float64(fma(fma(fma(Float64(0.0001789971 * x_m), x_m, 0.0005064034), t_2, Float64(fma(0.0072644182, t_0, fma(Float64(0.0424060604 * x_m), x_m, 0.1049934947)) * Float64(x_m * x_m))), x_m, x_m) / fma(Float64(x_m * x_m), fma(0.0008327945, t_2, Float64(Float64(Float64(2.0 * 0.0001789971) * Float64(x_m * x_m)) * Float64(Float64(t_1 * Float64(x_m * x_m)) * t_1))), fma(0.0140005442, t_2, fma(0.0694555761, (t_1 ^ 2.0), fma(Float64(x_m * x_m), Float64(0.7715471019 + Float64(Float64(0.2909738639 * x_m) * x_m)), 1.0)))));
	else
		tmp = Float64(x_m / fma(fma(Float64(2.0 * 0.0001789971), Float64(x_m * x_m), 0.0008327945), (Float64(t_0 * x_m) ^ 2.0), fma(0.0140005442, Float64(Float64(t_1 * t_1) * Float64(x_m * x_m)), fma(fma(0.0694555761, t_0, fma(Float64(0.2909738639 * x_m), x_m, 0.7715471019)), Float64(x_m * x_m), 1.0))));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[Power[N[(x$95$m * x$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$0, 2.0], $MachinePrecision]}, N[(x$95$s * If[LessEqual[x$95$m, 1e+26], N[(N[(N[(N[(N[(0.0001789971 * x$95$m), $MachinePrecision] * x$95$m + 0.0005064034), $MachinePrecision] * t$95$2 + N[(N[(0.0072644182 * t$95$0 + N[(N[(0.0424060604 * x$95$m), $MachinePrecision] * x$95$m + 0.1049934947), $MachinePrecision]), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision] / N[(N[(x$95$m * x$95$m), $MachinePrecision] * N[(0.0008327945 * t$95$2 + N[(N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$1 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * t$95$2 + N[(0.0694555761 * N[Power[t$95$1, 2.0], $MachinePrecision] + N[(N[(x$95$m * x$95$m), $MachinePrecision] * N[(0.7715471019 + N[(N[(0.2909738639 * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 0.0008327945), $MachinePrecision] * N[Power[N[(t$95$0 * x$95$m), $MachinePrecision], 2.0], $MachinePrecision] + N[(0.0140005442 * N[(N[(t$95$1 * t$95$1), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0694555761 * t$95$0 + N[(N[(0.2909738639 * x$95$m), $MachinePrecision] * x$95$m + 0.7715471019), $MachinePrecision]), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000005e26

   1. Initial program 71.3%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\frac{1789971}{10000000000} \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \frac{2532017}{5000000000}, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \frac{36322091}{5000000000}, \mathsf{fma}\left(x \cdot x, \frac{1049934947}{10000000000} + \left(\frac{106015151}{2500000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{1665589}{2000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot \frac{1789971}{10000000000}\right) \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{{x}^{8}}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, \frac{7715471019}{10000000000} + \left(\frac{2909738639}{10000000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 71.3%

      \[\leadsto \frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{\left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   9. Applied rewrites 71.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x, x, 0.0005064034\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0072644182, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.0424060604 \cdot x, x, 0.1049934947\right)\right) \cdot \left(x \cdot x\right)\right), x, 1 \cdot x\right)}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   if 1.00000000000000005e26 < x

   1. Initial program 0.1%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 0.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{1665589}{2000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot \frac{1789971}{10000000000}\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, \frac{7715471019}{10000000000} + \left(\frac{2909738639}{10000000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 5.1%

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   9. Applied rewrites 5.1%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)}} \]

   10. Taylor expanded in x around 0

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot \frac{1789971}{10000000000}, x \cdot x, \frac{1665589}{2000000000}\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{70002721}{5000000000}, \color{blue}{{x}^{8}}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{2909738639}{10000000000} \cdot x, x, \frac{7715471019}{10000000000}\right)\right), x \cdot x, 1\right)\right)\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 5.1%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, \color{blue}{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right)}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x, x, 0.0005064034\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0072644182, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.0424060604 \cdot x, x, 0.1049934947\right)\right) \cdot \left(x \cdot x\right)\right), x, x\right)}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right), \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := {\left(x\_m \cdot x\_m\right)}^{2}\\ t_1 := \left(x\_m \cdot x\_m\right) \cdot x\_m\\ t_2 := {t\_0}^{2}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x\_m, x\_m, 0.0005064034\right), t\_2, \mathsf{fma}\left(\mathsf{fma}\left(0.0072644182, t\_0, \mathsf{fma}\left(0.0424060604 \cdot x\_m, x\_m, 0.1049934947\right)\right), x\_m \cdot x\_m, 1\right)\right) \cdot x\_m}{\mathsf{fma}\left(x\_m \cdot x\_m, \mathsf{fma}\left(0.0008327945, t\_2, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x\_m \cdot x\_m\right)\right) \cdot \left(\left(t\_1 \cdot \left(x\_m \cdot x\_m\right)\right) \cdot t\_1\right)\right), \mathsf{fma}\left(0.0140005442, t\_2, \mathsf{fma}\left(0.0694555761, {t\_1}^{2}, \mathsf{fma}\left(x\_m \cdot x\_m, 0.7715471019 + \left(0.2909738639 \cdot x\_m\right) \cdot x\_m, 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x\_m \cdot x\_m, 0.0008327945\right), {\left(t\_0 \cdot x\_m\right)}^{2}, \mathsf{fma}\left(0.0140005442, \left(t\_1 \cdot t\_1\right) \cdot \left(x\_m \cdot x\_m\right), \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, t\_0, \mathsf{fma}\left(0.2909738639 \cdot x\_m, x\_m, 0.7715471019\right)\right), x\_m \cdot x\_m, 1\right)\right)\right)}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (pow (* x_m x_m) 2.0))
        (t_1 (* (* x_m x_m) x_m))
        (t_2 (pow t_0 2.0)))
   (*
    x_s
    (if (<= x_m 1e+26)
      (/
       (*
        (fma
         (fma (* 0.0001789971 x_m) x_m 0.0005064034)
         t_2
         (fma
          (fma 0.0072644182 t_0 (fma (* 0.0424060604 x_m) x_m 0.1049934947))
          (* x_m x_m)
          1.0))
        x_m)
       (fma
        (* x_m x_m)
        (fma
         0.0008327945
         t_2
         (* (* (* 2.0 0.0001789971) (* x_m x_m)) (* (* t_1 (* x_m x_m)) t_1)))
        (fma
         0.0140005442
         t_2
         (fma
          0.0694555761
          (pow t_1 2.0)
          (fma
           (* x_m x_m)
           (+ 0.7715471019 (* (* 0.2909738639 x_m) x_m))
           1.0)))))
      (/
       x_m
       (fma
        (fma (* 2.0 0.0001789971) (* x_m x_m) 0.0008327945)
        (pow (* t_0 x_m) 2.0)
        (fma
         0.0140005442
         (* (* t_1 t_1) (* x_m x_m))
         (fma
          (fma 0.0694555761 t_0 (fma (* 0.2909738639 x_m) x_m 0.7715471019))
          (* x_m x_m)
          1.0))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = pow((x_m * x_m), 2.0);
	double t_1 = (x_m * x_m) * x_m;
	double t_2 = pow(t_0, 2.0);
	double tmp;
	if (x_m <= 1e+26) {
		tmp = (fma(fma((0.0001789971 * x_m), x_m, 0.0005064034), t_2, fma(fma(0.0072644182, t_0, fma((0.0424060604 * x_m), x_m, 0.1049934947)), (x_m * x_m), 1.0)) * x_m) / fma((x_m * x_m), fma(0.0008327945, t_2, (((2.0 * 0.0001789971) * (x_m * x_m)) * ((t_1 * (x_m * x_m)) * t_1))), fma(0.0140005442, t_2, fma(0.0694555761, pow(t_1, 2.0), fma((x_m * x_m), (0.7715471019 + ((0.2909738639 * x_m) * x_m)), 1.0))));
	} else {
		tmp = x_m / fma(fma((2.0 * 0.0001789971), (x_m * x_m), 0.0008327945), pow((t_0 * x_m), 2.0), fma(0.0140005442, ((t_1 * t_1) * (x_m * x_m)), fma(fma(0.0694555761, t_0, fma((0.2909738639 * x_m), x_m, 0.7715471019)), (x_m * x_m), 1.0)));
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(x_m * x_m) ^ 2.0
	t_1 = Float64(Float64(x_m * x_m) * x_m)
	t_2 = t_0 ^ 2.0
	tmp = 0.0
	if (x_m <= 1e+26)
		tmp = Float64(Float64(fma(fma(Float64(0.0001789971 * x_m), x_m, 0.0005064034), t_2, fma(fma(0.0072644182, t_0, fma(Float64(0.0424060604 * x_m), x_m, 0.1049934947)), Float64(x_m * x_m), 1.0)) * x_m) / fma(Float64(x_m * x_m), fma(0.0008327945, t_2, Float64(Float64(Float64(2.0 * 0.0001789971) * Float64(x_m * x_m)) * Float64(Float64(t_1 * Float64(x_m * x_m)) * t_1))), fma(0.0140005442, t_2, fma(0.0694555761, (t_1 ^ 2.0), fma(Float64(x_m * x_m), Float64(0.7715471019 + Float64(Float64(0.2909738639 * x_m) * x_m)), 1.0)))));
	else
		tmp = Float64(x_m / fma(fma(Float64(2.0 * 0.0001789971), Float64(x_m * x_m), 0.0008327945), (Float64(t_0 * x_m) ^ 2.0), fma(0.0140005442, Float64(Float64(t_1 * t_1) * Float64(x_m * x_m)), fma(fma(0.0694555761, t_0, fma(Float64(0.2909738639 * x_m), x_m, 0.7715471019)), Float64(x_m * x_m), 1.0))));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[Power[N[(x$95$m * x$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]}, Block[{t$95$2 = N[Power[t$95$0, 2.0], $MachinePrecision]}, N[(x$95$s * If[LessEqual[x$95$m, 1e+26], N[(N[(N[(N[(N[(0.0001789971 * x$95$m), $MachinePrecision] * x$95$m + 0.0005064034), $MachinePrecision] * t$95$2 + N[(N[(0.0072644182 * t$95$0 + N[(N[(0.0424060604 * x$95$m), $MachinePrecision] * x$95$m + 0.1049934947), $MachinePrecision]), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision] / N[(N[(x$95$m * x$95$m), $MachinePrecision] * N[(0.0008327945 * t$95$2 + N[(N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$1 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * t$95$2 + N[(0.0694555761 * N[Power[t$95$1, 2.0], $MachinePrecision] + N[(N[(x$95$m * x$95$m), $MachinePrecision] * N[(0.7715471019 + N[(N[(0.2909738639 * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 0.0008327945), $MachinePrecision] * N[Power[N[(t$95$0 * x$95$m), $MachinePrecision], 2.0], $MachinePrecision] + N[(0.0140005442 * N[(N[(t$95$1 * t$95$1), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0694555761 * t$95$0 + N[(N[(0.2909738639 * x$95$m), $MachinePrecision] * x$95$m + 0.7715471019), $MachinePrecision]), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000005e26

   1. Initial program 71.3%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\frac{1789971}{10000000000} \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \frac{2532017}{5000000000}, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \frac{36322091}{5000000000}, \mathsf{fma}\left(x \cdot x, \frac{1049934947}{10000000000} + \left(\frac{106015151}{2500000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{1665589}{2000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot \frac{1789971}{10000000000}\right) \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{{x}^{8}}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, \frac{7715471019}{10000000000} + \left(\frac{2909738639}{10000000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 71.3%

      \[\leadsto \frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \color{blue}{\left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   9. Applied rewrites 71.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x, x, 0.0005064034\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\mathsf{fma}\left(0.0072644182, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.0424060604 \cdot x, x, 0.1049934947\right)\right), x \cdot x, 1\right)\right) \cdot x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   if 1.00000000000000005e26 < x

   1. Initial program 0.1%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 0.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{1665589}{2000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot \frac{1789971}{10000000000}\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, \frac{7715471019}{10000000000} + \left(\frac{2909738639}{10000000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 5.1%

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   9. Applied rewrites 5.1%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)}} \]

   10. Taylor expanded in x around 0

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot \frac{1789971}{10000000000}, x \cdot x, \frac{1665589}{2000000000}\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{70002721}{5000000000}, \color{blue}{{x}^{8}}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{2909738639}{10000000000} \cdot x, x, \frac{7715471019}{10000000000}\right)\right), x \cdot x, 1\right)\right)\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 5.1%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, \color{blue}{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right)}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 56.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := {\left(x\_m \cdot x\_m\right)}^{2}\\ t_1 := \left(x\_m \cdot x\_m\right) \cdot x\_m\\ t_2 := \left(t\_1 \cdot t\_1\right) \cdot \left(x\_m \cdot x\_m\right)\\ t_3 := \mathsf{fma}\left(0.0694555761, t\_0, \mathsf{fma}\left(0.2909738639 \cdot x\_m, x\_m, 0.7715471019\right)\right)\\ t_4 := {\left(t\_0 \cdot x\_m\right)}^{2}\\ t_5 := \mathsf{fma}\left(2 \cdot 0.0001789971, x\_m \cdot x\_m, 0.0008327945\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{+26}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x\_m, x\_m, 0.0005064034\right), {t\_0}^{2}, \mathsf{fma}\left(0.0072644182, t\_0, \mathsf{fma}\left(0.0424060604 \cdot x\_m, x\_m, 0.1049934947\right)\right) \cdot \left(x\_m \cdot x\_m\right)\right), x\_m, x\_m\right)}{\mathsf{fma}\left(t\_4, t\_5, \mathsf{fma}\left(0.0140005442, t\_2, \mathsf{fma}\left(x\_m \cdot x\_m, t\_3, 1\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\mathsf{fma}\left(t\_5, t\_4, \mathsf{fma}\left(0.0140005442, t\_2, \mathsf{fma}\left(t\_3, x\_m \cdot x\_m, 1\right)\right)\right)}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (pow (* x_m x_m) 2.0))
        (t_1 (* (* x_m x_m) x_m))
        (t_2 (* (* t_1 t_1) (* x_m x_m)))
        (t_3
         (fma 0.0694555761 t_0 (fma (* 0.2909738639 x_m) x_m 0.7715471019)))
        (t_4 (pow (* t_0 x_m) 2.0))
        (t_5 (fma (* 2.0 0.0001789971) (* x_m x_m) 0.0008327945)))
   (*
    x_s
    (if (<= x_m 1e+26)
      (/
       (fma
        (fma
         (fma (* 0.0001789971 x_m) x_m 0.0005064034)
         (pow t_0 2.0)
         (*
          (fma 0.0072644182 t_0 (fma (* 0.0424060604 x_m) x_m 0.1049934947))
          (* x_m x_m)))
        x_m
        x_m)
       (fma t_4 t_5 (fma 0.0140005442 t_2 (fma (* x_m x_m) t_3 1.0))))
      (/
       x_m
       (fma t_5 t_4 (fma 0.0140005442 t_2 (fma t_3 (* x_m x_m) 1.0))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = pow((x_m * x_m), 2.0);
	double t_1 = (x_m * x_m) * x_m;
	double t_2 = (t_1 * t_1) * (x_m * x_m);
	double t_3 = fma(0.0694555761, t_0, fma((0.2909738639 * x_m), x_m, 0.7715471019));
	double t_4 = pow((t_0 * x_m), 2.0);
	double t_5 = fma((2.0 * 0.0001789971), (x_m * x_m), 0.0008327945);
	double tmp;
	if (x_m <= 1e+26) {
		tmp = fma(fma(fma((0.0001789971 * x_m), x_m, 0.0005064034), pow(t_0, 2.0), (fma(0.0072644182, t_0, fma((0.0424060604 * x_m), x_m, 0.1049934947)) * (x_m * x_m))), x_m, x_m) / fma(t_4, t_5, fma(0.0140005442, t_2, fma((x_m * x_m), t_3, 1.0)));
	} else {
		tmp = x_m / fma(t_5, t_4, fma(0.0140005442, t_2, fma(t_3, (x_m * x_m), 1.0)));
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(x_m * x_m) ^ 2.0
	t_1 = Float64(Float64(x_m * x_m) * x_m)
	t_2 = Float64(Float64(t_1 * t_1) * Float64(x_m * x_m))
	t_3 = fma(0.0694555761, t_0, fma(Float64(0.2909738639 * x_m), x_m, 0.7715471019))
	t_4 = Float64(t_0 * x_m) ^ 2.0
	t_5 = fma(Float64(2.0 * 0.0001789971), Float64(x_m * x_m), 0.0008327945)
	tmp = 0.0
	if (x_m <= 1e+26)
		tmp = Float64(fma(fma(fma(Float64(0.0001789971 * x_m), x_m, 0.0005064034), (t_0 ^ 2.0), Float64(fma(0.0072644182, t_0, fma(Float64(0.0424060604 * x_m), x_m, 0.1049934947)) * Float64(x_m * x_m))), x_m, x_m) / fma(t_4, t_5, fma(0.0140005442, t_2, fma(Float64(x_m * x_m), t_3, 1.0))));
	else
		tmp = Float64(x_m / fma(t_5, t_4, fma(0.0140005442, t_2, fma(t_3, Float64(x_m * x_m), 1.0))));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[Power[N[(x$95$m * x$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 * t$95$1), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(0.0694555761 * t$95$0 + N[(N[(0.2909738639 * x$95$m), $MachinePrecision] * x$95$m + 0.7715471019), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Power[N[(t$95$0 * x$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$5 = N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 0.0008327945), $MachinePrecision]}, N[(x$95$s * If[LessEqual[x$95$m, 1e+26], N[(N[(N[(N[(N[(0.0001789971 * x$95$m), $MachinePrecision] * x$95$m + 0.0005064034), $MachinePrecision] * N[Power[t$95$0, 2.0], $MachinePrecision] + N[(N[(0.0072644182 * t$95$0 + N[(N[(0.0424060604 * x$95$m), $MachinePrecision] * x$95$m + 0.1049934947), $MachinePrecision]), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision] / N[(t$95$4 * t$95$5 + N[(0.0140005442 * t$95$2 + N[(N[(x$95$m * x$95$m), $MachinePrecision] * t$95$3 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(t$95$5 * t$95$4 + N[(0.0140005442 * t$95$2 + N[(t$95$3 * N[(x$95$m * x$95$m), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000005e26

   1. Initial program 71.3%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2} \cdot \left(x \cdot x\right), \frac{0.0001789971}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}, \frac{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}\right)} \cdot x \]

   6. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0001789971 \cdot x, x, 0.0005064034\right), \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0072644182, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.0424060604 \cdot x, x, 0.1049934947\right)\right), 1\right)\right) \cdot x}{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), 1\right)\right)\right)}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{1789971}{10000000000} \cdot x, x, \frac{2532017}{5000000000}\right), \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{36322091}{5000000000}, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{106015151}{2500000000} \cdot x, x, \frac{1049934947}{10000000000}\right)\right), 1\right)\right) \cdot x}{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(2 \cdot \frac{1789971}{10000000000}, x \cdot x, \frac{1665589}{2000000000}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, \color{blue}{{x}^{8}}, \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{2909738639}{10000000000} \cdot x, x, \frac{7715471019}{10000000000}\right)\right), 1\right)\right)\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 71.2%

      \[\leadsto \frac{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0001789971 \cdot x, x, 0.0005064034\right), \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0072644182, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.0424060604 \cdot x, x, 0.1049934947\right)\right), 1\right)\right) \cdot x}{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), \mathsf{fma}\left(0.0140005442, \color{blue}{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right)}, \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), 1\right)\right)\right)} \]

   11. Applied rewrites 71.3%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0001789971 \cdot x, x, 0.0005064034\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0072644182, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.0424060604 \cdot x, x, 0.1049934947\right)\right) \cdot \left(x \cdot x\right)\right), x, x\right)}}{\mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), \mathsf{fma}\left(0.0140005442, \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right), \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), 1\right)\right)\right)} \]

   if 1.00000000000000005e26 < x

   1. Initial program 0.1%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 0.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{1665589}{2000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot \frac{1789971}{10000000000}\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, \frac{7715471019}{10000000000} + \left(\frac{2909738639}{10000000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 5.1%

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   9. Applied rewrites 5.1%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)}} \]

   10. Taylor expanded in x around 0

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot \frac{1789971}{10000000000}, x \cdot x, \frac{1665589}{2000000000}\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{70002721}{5000000000}, \color{blue}{{x}^{8}}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{2909738639}{10000000000} \cdot x, x, \frac{7715471019}{10000000000}\right)\right), x \cdot x, 1\right)\right)\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 5.1%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, \color{blue}{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right)}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 56.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \left(x\_m \cdot x\_m\right) \cdot \left(x\_m \cdot x\_m\right)\\ t_1 := \left(x\_m \cdot x\_m\right) \cdot x\_m\\ t_2 := t\_0 \cdot \left(x\_m \cdot x\_m\right)\\ t_3 := t\_2 \cdot \left(x\_m \cdot x\_m\right)\\ t_4 := t\_3 \cdot \left(x\_m \cdot x\_m\right)\\ t_5 := {\left(x\_m \cdot x\_m\right)}^{2}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x\_m \cdot x\_m\right)\right) + 0.0424060604 \cdot t\_0\right) + 0.0072644182 \cdot t\_2\right) + 0.0005064034 \cdot t\_3\right) + 0.0001789971 \cdot t\_4}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x\_m \cdot x\_m\right)\right) + 0.2909738639 \cdot t\_0\right) + 0.0694555761 \cdot t\_2\right) + 0.0140005442 \cdot t\_3\right) + 0.0008327945 \cdot t\_4\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(t\_4 \cdot \left(x\_m \cdot x\_m\right)\right)} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x\_m \cdot x\_m, 0.0008327945\right), {\left(t\_5 \cdot x\_m\right)}^{2}, \mathsf{fma}\left(0.0140005442, \left(t\_1 \cdot t\_1\right) \cdot \left(x\_m \cdot x\_m\right), \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, t\_5, \mathsf{fma}\left(0.2909738639 \cdot x\_m, x\_m, 0.7715471019\right)\right), x\_m \cdot x\_m, 1\right)\right)\right)}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (* (* x_m x_m) (* x_m x_m)))
        (t_1 (* (* x_m x_m) x_m))
        (t_2 (* t_0 (* x_m x_m)))
        (t_3 (* t_2 (* x_m x_m)))
        (t_4 (* t_3 (* x_m x_m)))
        (t_5 (pow (* x_m x_m) 2.0)))
   (*
    x_s
    (if (<= x_m 5e+25)
      (*
       (/
        (+
         (+
          (+
           (+ (+ 1.0 (* 0.1049934947 (* x_m x_m))) (* 0.0424060604 t_0))
           (* 0.0072644182 t_2))
          (* 0.0005064034 t_3))
         (* 0.0001789971 t_4))
        (+
         (+
          (+
           (+
            (+ (+ 1.0 (* 0.7715471019 (* x_m x_m))) (* 0.2909738639 t_0))
            (* 0.0694555761 t_2))
           (* 0.0140005442 t_3))
          (* 0.0008327945 t_4))
         (* (* 2.0 0.0001789971) (* t_4 (* x_m x_m)))))
       x_m)
      (/
       x_m
       (fma
        (fma (* 2.0 0.0001789971) (* x_m x_m) 0.0008327945)
        (pow (* t_5 x_m) 2.0)
        (fma
         0.0140005442
         (* (* t_1 t_1) (* x_m x_m))
         (fma
          (fma 0.0694555761 t_5 (fma (* 0.2909738639 x_m) x_m 0.7715471019))
          (* x_m x_m)
          1.0))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = (x_m * x_m) * (x_m * x_m);
	double t_1 = (x_m * x_m) * x_m;
	double t_2 = t_0 * (x_m * x_m);
	double t_3 = t_2 * (x_m * x_m);
	double t_4 = t_3 * (x_m * x_m);
	double t_5 = pow((x_m * x_m), 2.0);
	double tmp;
	if (x_m <= 5e+25) {
		tmp = ((((((1.0 + (0.1049934947 * (x_m * x_m))) + (0.0424060604 * t_0)) + (0.0072644182 * t_2)) + (0.0005064034 * t_3)) + (0.0001789971 * t_4)) / ((((((1.0 + (0.7715471019 * (x_m * x_m))) + (0.2909738639 * t_0)) + (0.0694555761 * t_2)) + (0.0140005442 * t_3)) + (0.0008327945 * t_4)) + ((2.0 * 0.0001789971) * (t_4 * (x_m * x_m))))) * x_m;
	} else {
		tmp = x_m / fma(fma((2.0 * 0.0001789971), (x_m * x_m), 0.0008327945), pow((t_5 * x_m), 2.0), fma(0.0140005442, ((t_1 * t_1) * (x_m * x_m)), fma(fma(0.0694555761, t_5, fma((0.2909738639 * x_m), x_m, 0.7715471019)), (x_m * x_m), 1.0)));
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(Float64(x_m * x_m) * Float64(x_m * x_m))
	t_1 = Float64(Float64(x_m * x_m) * x_m)
	t_2 = Float64(t_0 * Float64(x_m * x_m))
	t_3 = Float64(t_2 * Float64(x_m * x_m))
	t_4 = Float64(t_3 * Float64(x_m * x_m))
	t_5 = Float64(x_m * x_m) ^ 2.0
	tmp = 0.0
	if (x_m <= 5e+25)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.1049934947 * Float64(x_m * x_m))) + Float64(0.0424060604 * t_0)) + Float64(0.0072644182 * t_2)) + Float64(0.0005064034 * t_3)) + Float64(0.0001789971 * t_4)) / Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.7715471019 * Float64(x_m * x_m))) + Float64(0.2909738639 * t_0)) + Float64(0.0694555761 * t_2)) + Float64(0.0140005442 * t_3)) + Float64(0.0008327945 * t_4)) + Float64(Float64(2.0 * 0.0001789971) * Float64(t_4 * Float64(x_m * x_m))))) * x_m);
	else
		tmp = Float64(x_m / fma(fma(Float64(2.0 * 0.0001789971), Float64(x_m * x_m), 0.0008327945), (Float64(t_5 * x_m) ^ 2.0), fma(0.0140005442, Float64(Float64(t_1 * t_1) * Float64(x_m * x_m)), fma(fma(0.0694555761, t_5, fma(Float64(0.2909738639 * x_m), x_m, 0.7715471019)), Float64(x_m * x_m), 1.0))));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[(N[(x$95$m * x$95$m), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x$95$m * x$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Power[N[(x$95$m * x$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, N[(x$95$s * If[LessEqual[x$95$m, 5e+25], N[(N[(N[(N[(N[(N[(N[(1.0 + N[(0.1049934947 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0424060604 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0072644182 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0005064034 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(0.0001789971 * t$95$4), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(1.0 + N[(0.7715471019 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.2909738639 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0694555761 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(0.0008327945 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(t$95$4 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], N[(x$95$m / N[(N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 0.0008327945), $MachinePrecision] * N[Power[N[(t$95$5 * x$95$m), $MachinePrecision], 2.0], $MachinePrecision] + N[(0.0140005442 * N[(N[(t$95$1 * t$95$1), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision] + N[(N[(0.0694555761 * t$95$5 + N[(N[(0.2909738639 * x$95$m), $MachinePrecision] * x$95$m + 0.7715471019), $MachinePrecision]), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000024e25

   1. Initial program 71.3%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   if 5.00000000000000024e25 < x

   1. Initial program 0.1%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   4. Applied rewrites 0.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.0001789971 \cdot \left(x \cdot x\right), {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left({\left({\left(x \cdot x\right)}^{2}\right)}^{2}, 0.0005064034, \mathsf{fma}\left({\left(\left(x \cdot x\right) \cdot x\right)}^{2}, 0.0072644182, \mathsf{fma}\left(x \cdot x, 0.1049934947 + \left(0.0424060604 \cdot x\right) \cdot x, 1\right)\right)\right)\right) \cdot x}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\frac{1665589}{2000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot \frac{1789971}{10000000000}\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(\frac{70002721}{5000000000}, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, \frac{7715471019}{10000000000} + \left(\frac{2909738639}{10000000000} \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 5.1%

      \[\leadsto \frac{\color{blue}{x}}{\mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(0.0008327945, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right) \cdot {\left({\left(x \cdot x\right)}^{2}\right)}^{2}\right), \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(0.0694555761, {\left(\left(x \cdot x\right) \cdot x\right)}^{2}, \mathsf{fma}\left(x \cdot x, 0.7715471019 + \left(0.2909738639 \cdot x\right) \cdot x, 1\right)\right)\right)\right)} \]

   9. Applied rewrites 5.1%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, {\left({\left(x \cdot x\right)}^{2}\right)}^{2}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)}} \]

   10. Taylor expanded in x around 0

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot \frac{1789971}{10000000000}, x \cdot x, \frac{1665589}{2000000000}\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{70002721}{5000000000}, \color{blue}{{x}^{8}}, \mathsf{fma}\left(\mathsf{fma}\left(\frac{694555761}{10000000000}, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(\frac{2909738639}{10000000000} \cdot x, x, \frac{7715471019}{10000000000}\right)\right), x \cdot x, 1\right)\right)\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 5.1%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(2 \cdot 0.0001789971, x \cdot x, 0.0008327945\right), {\left({\left(x \cdot x\right)}^{2} \cdot x\right)}^{2}, \mathsf{fma}\left(0.0140005442, \color{blue}{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \left(x \cdot x\right)}, \mathsf{fma}\left(\mathsf{fma}\left(0.0694555761, {\left(x \cdot x\right)}^{2}, \mathsf{fma}\left(0.2909738639 \cdot x, x, 0.7715471019\right)\right), x \cdot x, 1\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \left(x\_m \cdot x\_m\right) \cdot \left(x\_m \cdot x\_m\right)\\ t_1 := t\_0 \cdot \left(x\_m \cdot x\_m\right)\\ t_2 := t\_1 \cdot \left(x\_m \cdot x\_m\right)\\ t_3 := t\_2 \cdot \left(x\_m \cdot x\_m\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x\_m \cdot x\_m\right)\right) + 0.0424060604 \cdot t\_0\right) + 0.0072644182 \cdot t\_1\right) + 0.0005064034 \cdot t\_2\right) + 0.0001789971 \cdot t\_3}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x\_m \cdot x\_m\right)\right) + 0.2909738639 \cdot t\_0\right) + 0.0694555761 \cdot t\_1\right) + 0.0140005442 \cdot t\_2\right) + 0.0008327945 \cdot t\_3\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(t\_3 \cdot \left(x\_m \cdot x\_m\right)\right)} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m)
 :precision binary64
 (let* ((t_0 (* (* x_m x_m) (* x_m x_m)))
        (t_1 (* t_0 (* x_m x_m)))
        (t_2 (* t_1 (* x_m x_m)))
        (t_3 (* t_2 (* x_m x_m))))
   (*
    x_s
    (if (<= x_m 5e+25)
      (*
       (/
        (+
         (+
          (+
           (+ (+ 1.0 (* 0.1049934947 (* x_m x_m))) (* 0.0424060604 t_0))
           (* 0.0072644182 t_1))
          (* 0.0005064034 t_2))
         (* 0.0001789971 t_3))
        (+
         (+
          (+
           (+
            (+ (+ 1.0 (* 0.7715471019 (* x_m x_m))) (* 0.2909738639 t_0))
            (* 0.0694555761 t_1))
           (* 0.0140005442 t_2))
          (* 0.0008327945 t_3))
         (* (* 2.0 0.0001789971) (* t_3 (* x_m x_m)))))
       x_m)
      x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	double t_0 = (x_m * x_m) * (x_m * x_m);
	double t_1 = t_0 * (x_m * x_m);
	double t_2 = t_1 * (x_m * x_m);
	double t_3 = t_2 * (x_m * x_m);
	double tmp;
	if (x_m <= 5e+25) {
		tmp = ((((((1.0 + (0.1049934947 * (x_m * x_m))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x_m * x_m))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x_m * x_m))))) * x_m;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x_m * x_m) * (x_m * x_m)
    t_1 = t_0 * (x_m * x_m)
    t_2 = t_1 * (x_m * x_m)
    t_3 = t_2 * (x_m * x_m)
    if (x_m <= 5d+25) then
        tmp = ((((((1.0d0 + (0.1049934947d0 * (x_m * x_m))) + (0.0424060604d0 * t_0)) + (0.0072644182d0 * t_1)) + (0.0005064034d0 * t_2)) + (0.0001789971d0 * t_3)) / ((((((1.0d0 + (0.7715471019d0 * (x_m * x_m))) + (0.2909738639d0 * t_0)) + (0.0694555761d0 * t_1)) + (0.0140005442d0 * t_2)) + (0.0008327945d0 * t_3)) + ((2.0d0 * 0.0001789971d0) * (t_3 * (x_m * x_m))))) * x_m
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	double t_0 = (x_m * x_m) * (x_m * x_m);
	double t_1 = t_0 * (x_m * x_m);
	double t_2 = t_1 * (x_m * x_m);
	double t_3 = t_2 * (x_m * x_m);
	double tmp;
	if (x_m <= 5e+25) {
		tmp = ((((((1.0 + (0.1049934947 * (x_m * x_m))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x_m * x_m))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x_m * x_m))))) * x_m;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m):
	t_0 = (x_m * x_m) * (x_m * x_m)
	t_1 = t_0 * (x_m * x_m)
	t_2 = t_1 * (x_m * x_m)
	t_3 = t_2 * (x_m * x_m)
	tmp = 0
	if x_m <= 5e+25:
		tmp = ((((((1.0 + (0.1049934947 * (x_m * x_m))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x_m * x_m))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x_m * x_m))))) * x_m
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	t_0 = Float64(Float64(x_m * x_m) * Float64(x_m * x_m))
	t_1 = Float64(t_0 * Float64(x_m * x_m))
	t_2 = Float64(t_1 * Float64(x_m * x_m))
	t_3 = Float64(t_2 * Float64(x_m * x_m))
	tmp = 0.0
	if (x_m <= 5e+25)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.1049934947 * Float64(x_m * x_m))) + Float64(0.0424060604 * t_0)) + Float64(0.0072644182 * t_1)) + Float64(0.0005064034 * t_2)) + Float64(0.0001789971 * t_3)) / Float64(Float64(Float64(Float64(Float64(Float64(1.0 + Float64(0.7715471019 * Float64(x_m * x_m))) + Float64(0.2909738639 * t_0)) + Float64(0.0694555761 * t_1)) + Float64(0.0140005442 * t_2)) + Float64(0.0008327945 * t_3)) + Float64(Float64(2.0 * 0.0001789971) * Float64(t_3 * Float64(x_m * x_m))))) * x_m);
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m)
	t_0 = (x_m * x_m) * (x_m * x_m);
	t_1 = t_0 * (x_m * x_m);
	t_2 = t_1 * (x_m * x_m);
	t_3 = t_2 * (x_m * x_m);
	tmp = 0.0;
	if (x_m <= 5e+25)
		tmp = ((((((1.0 + (0.1049934947 * (x_m * x_m))) + (0.0424060604 * t_0)) + (0.0072644182 * t_1)) + (0.0005064034 * t_2)) + (0.0001789971 * t_3)) / ((((((1.0 + (0.7715471019 * (x_m * x_m))) + (0.2909738639 * t_0)) + (0.0694555761 * t_1)) + (0.0140005442 * t_2)) + (0.0008327945 * t_3)) + ((2.0 * 0.0001789971) * (t_3 * (x_m * x_m))))) * x_m;
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := Block[{t$95$0 = N[(N[(x$95$m * x$95$m), $MachinePrecision] * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[x$95$m, 5e+25], N[(N[(N[(N[(N[(N[(N[(1.0 + N[(0.1049934947 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.0424060604 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0072644182 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(0.0005064034 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0001789971 * t$95$3), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(1.0 + N[(0.7715471019 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.2909738639 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(0.0694555761 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(0.0140005442 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(0.0008327945 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 * 0.0001789971), $MachinePrecision] * N[(t$95$3 * N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], x$95$m]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000024e25

   1. Initial program 71.3%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   if 5.00000000000000024e25 < x

   1. Initial program 0.1%

      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 3.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 51.3% accurate, 415.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m) {
	return x_s * x_m;
}

Fortran

x\_m =     private
x\_s =     private
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_s, x_m)
use fmin_fmax_functions
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    code = x_s * x_m
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m) {
	return x_s * x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m)
	return Float64(x_s * x_m)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m)
	tmp = x_s * x_m;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 54.3%

   \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 54.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025021 
(FPCore (x)
  :name "Jmat.Real.dawson"
  :precision binary64
  (* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))