Jmat.Real.erf

Percentage Accurate: 79.7% → 80.8%

Time: 25.1s

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} t_0 := \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\\ 1 - \left(t\_0 \cdot \left(\frac{31853699}{125000000} + t\_0 \cdot \left(\frac{-8890523}{31250000} + t\_0 \cdot \left(\frac{1421413741}{1000000000} + t\_0 \cdot \left(\frac{-1453152027}{1000000000} + t\_0 \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (/ 1 (+ 1 (* 3275911/10000000 (fabs x))))))
  (-
   1
   (*
    (*
     t_0
     (+
      31853699/125000000
      (*
       t_0
       (+
        -8890523/31250000
        (*
         t_0
         (+
          1421413741/1000000000
          (*
           t_0
           (+
            -1453152027/1000000000
            (* t_0 1061405429/1000000000)))))))))
    (exp (- (* (fabs x) (fabs x))))))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[(1 / N[(1 + N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(1 - N[(N[(t$95$0 * N[(31853699/125000000 + N[(t$95$0 * N[(-8890523/31250000 + N[(t$95$0 * N[(1421413741/1000000000 + N[(t$95$0 * N[(-1453152027/1000000000 + N[(t$95$0 * 1061405429/1000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Initial Program: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \frac{1}{1 + \frac{3275911}{10000000} \cdot \left|x\right|}\\ 1 - \left(t\_0 \cdot \left(\frac{31853699}{125000000} + t\_0 \cdot \left(\frac{-8890523}{31250000} + t\_0 \cdot \left(\frac{1421413741}{1000000000} + t\_0 \cdot \left(\frac{-1453152027}{1000000000} + t\_0 \cdot \frac{1061405429}{1000000000}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (/ 1 (+ 1 (* 3275911/10000000 (fabs x))))))
  (-
   1
   (*
    (*
     t_0
     (+
      31853699/125000000
      (*
       t_0
       (+
        -8890523/31250000
        (*
         t_0
         (+
          1421413741/1000000000
          (*
           t_0
           (+
            -1453152027/1000000000
            (* t_0 1061405429/1000000000)))))))))
    (exp (- (* (fabs x) (fabs x))))))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[(1 / N[(1 + N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(1 - N[(N[(t$95$0 * N[(31853699/125000000 + N[(t$95$0 * N[(-8890523/31250000 + N[(t$95$0 * N[(1421413741/1000000000 + N[(t$95$0 * N[(-1453152027/1000000000 + N[(t$95$0 * 1061405429/1000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Exp[(-N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 80.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{-3275911}{10000000} \cdot \left|x\right|\\ t_1 := \frac{t\_0 \cdot t\_0 - 1 \cdot 1}{t\_0 + 1}\\ t_2 := \frac{3275911}{10000000} \cdot \left|x\right| - -1\\ t_3 := e^{x \cdot x}\\ t_4 := \frac{\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{\frac{1061405429}{1000000000}}{t\_2} - \frac{1453152027}{1000000000}}{t\_2} - \frac{-1421413741}{1000000000}}{t\_1}}{t\_1}}{t\_3 \cdot t\_2}\\ t_5 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_6 := -1 - t\_5\\ \frac{{1}^{3} - \frac{1}{\frac{{\left(t\_3 \cdot \left(t\_5 - -1\right)\right)}^{3}}{{\left(\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{t\_6}}{t\_6} - \frac{1421413741}{1000000000}}{1 - t\_0}}{t\_1}\right)}^{3}}}}{1 + \left({t\_4}^{2} + 1 \cdot t\_4\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* -3275911/10000000 (fabs x)))
       (t_1 (/ (- (* t_0 t_0) (* 1 1)) (+ t_0 1)))
       (t_2 (- (* 3275911/10000000 (fabs x)) -1))
       (t_3 (exp (* x x)))
       (t_4
        (/
         (-
          31853699/125000000
          (/
           (-
            -8890523/31250000
            (/
             (-
              (/
               (- (/ 1061405429/1000000000 t_2) 1453152027/1000000000)
               t_2)
              -1421413741/1000000000)
             t_1))
           t_1))
         (* t_3 t_2)))
       (t_5 (* (fabs x) 3275911/10000000))
       (t_6 (- -1 t_5)))
  (/
   (-
    (pow 1 3)
    (/
     1
     (/
      (pow (* t_3 (- t_5 -1)) 3)
      (pow
       (-
        31853699/125000000
        (/
         (-
          -8890523/31250000
          (/
           (-
            (/
             (- -1453152027/1000000000 (/ 1061405429/1000000000 t_6))
             t_6)
            1421413741/1000000000)
           (- 1 t_0)))
         t_1))
       3))))
   (+ 1 (+ (pow t_4 2) (* 1 t_4))))))

C

double code(double x) {
	double t_0 = -0.3275911 * fabs(x);
	double t_1 = ((t_0 * t_0) - (1.0 * 1.0)) / (t_0 + 1.0);
	double t_2 = (0.3275911 * fabs(x)) - -1.0;
	double t_3 = exp((x * x));
	double t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_1)) / t_1)) / (t_3 * t_2);
	double t_5 = fabs(x) * 0.3275911;
	double t_6 = -1.0 - t_5;
	return (pow(1.0, 3.0) - (1.0 / (pow((t_3 * (t_5 - -1.0)), 3.0) / pow((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_0))) / t_1)), 3.0)))) / (1.0 + (pow(t_4, 2.0) + (1.0 * t_4)));
}

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
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    t_0 = (-0.3275911d0) * abs(x)
    t_1 = ((t_0 * t_0) - (1.0d0 * 1.0d0)) / (t_0 + 1.0d0)
    t_2 = (0.3275911d0 * abs(x)) - (-1.0d0)
    t_3 = exp((x * x))
    t_4 = (0.254829592d0 - (((-0.284496736d0) - (((((1.061405429d0 / t_2) - 1.453152027d0) / t_2) - (-1.421413741d0)) / t_1)) / t_1)) / (t_3 * t_2)
    t_5 = abs(x) * 0.3275911d0
    t_6 = (-1.0d0) - t_5
    code = ((1.0d0 ** 3.0d0) - (1.0d0 / (((t_3 * (t_5 - (-1.0d0))) ** 3.0d0) / ((0.254829592d0 - (((-0.284496736d0) - (((((-1.453152027d0) - (1.061405429d0 / t_6)) / t_6) - 1.421413741d0) / (1.0d0 - t_0))) / t_1)) ** 3.0d0)))) / (1.0d0 + ((t_4 ** 2.0d0) + (1.0d0 * t_4)))
end function

Java

public static double code(double x) {
	double t_0 = -0.3275911 * Math.abs(x);
	double t_1 = ((t_0 * t_0) - (1.0 * 1.0)) / (t_0 + 1.0);
	double t_2 = (0.3275911 * Math.abs(x)) - -1.0;
	double t_3 = Math.exp((x * x));
	double t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_1)) / t_1)) / (t_3 * t_2);
	double t_5 = Math.abs(x) * 0.3275911;
	double t_6 = -1.0 - t_5;
	return (Math.pow(1.0, 3.0) - (1.0 / (Math.pow((t_3 * (t_5 - -1.0)), 3.0) / Math.pow((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_0))) / t_1)), 3.0)))) / (1.0 + (Math.pow(t_4, 2.0) + (1.0 * t_4)));
}

Python

def code(x):
	t_0 = -0.3275911 * math.fabs(x)
	t_1 = ((t_0 * t_0) - (1.0 * 1.0)) / (t_0 + 1.0)
	t_2 = (0.3275911 * math.fabs(x)) - -1.0
	t_3 = math.exp((x * x))
	t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_1)) / t_1)) / (t_3 * t_2)
	t_5 = math.fabs(x) * 0.3275911
	t_6 = -1.0 - t_5
	return (math.pow(1.0, 3.0) - (1.0 / (math.pow((t_3 * (t_5 - -1.0)), 3.0) / math.pow((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_0))) / t_1)), 3.0)))) / (1.0 + (math.pow(t_4, 2.0) + (1.0 * t_4)))

Julia

function code(x)
	t_0 = Float64(-0.3275911 * abs(x))
	t_1 = Float64(Float64(Float64(t_0 * t_0) - Float64(1.0 * 1.0)) / Float64(t_0 + 1.0))
	t_2 = Float64(Float64(0.3275911 * abs(x)) - -1.0)
	t_3 = exp(Float64(x * x))
	t_4 = Float64(Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(Float64(1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_1)) / t_1)) / Float64(t_3 * t_2))
	t_5 = Float64(abs(x) * 0.3275911)
	t_6 = Float64(-1.0 - t_5)
	return Float64(Float64((1.0 ^ 3.0) - Float64(1.0 / Float64((Float64(t_3 * Float64(t_5 - -1.0)) ^ 3.0) / (Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(-1.453152027 - Float64(1.061405429 / t_6)) / t_6) - 1.421413741) / Float64(1.0 - t_0))) / t_1)) ^ 3.0)))) / Float64(1.0 + Float64((t_4 ^ 2.0) + Float64(1.0 * t_4))))
end

MATLAB

function tmp = code(x)
	t_0 = -0.3275911 * abs(x);
	t_1 = ((t_0 * t_0) - (1.0 * 1.0)) / (t_0 + 1.0);
	t_2 = (0.3275911 * abs(x)) - -1.0;
	t_3 = exp((x * x));
	t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_1)) / t_1)) / (t_3 * t_2);
	t_5 = abs(x) * 0.3275911;
	t_6 = -1.0 - t_5;
	tmp = ((1.0 ^ 3.0) - (1.0 / (((t_3 * (t_5 - -1.0)) ^ 3.0) / ((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_0))) / t_1)) ^ 3.0)))) / (1.0 + ((t_4 ^ 2.0) + (1.0 * t_4)));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] - N[(1 * 1), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 + 1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(N[(1061405429/1000000000 / t$95$2), $MachinePrecision] - 1453152027/1000000000), $MachinePrecision] / t$95$2), $MachinePrecision] - -1421413741/1000000000), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$6 = N[(-1 - t$95$5), $MachinePrecision]}, N[(N[(N[Power[1, 3], $MachinePrecision] - N[(1 / N[(N[Power[N[(t$95$3 * N[(t$95$5 - -1), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision] / N[Power[N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(-1453152027/1000000000 - N[(1061405429/1000000000 / t$95$6), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / N[(1 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1 + N[(N[Power[t$95$4, 2], $MachinePrecision] + N[(1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 80.8%

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

   1. lift--.f64 N/A

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

   2. flip-- N/A

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

   3. lower-unsound-/.f64 N/A

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

   4. lower-unsound--.f64 N/A

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

   5. lower-unsound-*.f64 N/A

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

   6. lower-unsound-*.f64 N/A

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

   7. lower-unsound-+.f64 80.8%

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

9. Applied rewrites 80.8%

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

    1. lift--.f64 N/A

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

    2. flip-- N/A

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

    3. lower-unsound-/.f64 N/A

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

    4. lower-unsound--.f64 N/A

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

    5. lower-unsound-*.f64 N/A

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

    6. lower-unsound-*.f64 N/A

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

    7. lower-unsound-+.f64 80.8%

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

11. Applied rewrites 80.8%

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

    1. lift--.f64 N/A

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

    2. flip-- N/A

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

    3. lower-unsound-/.f64 N/A

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

    4. lower-unsound--.f64 N/A

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

    5. lower-unsound-*.f64 N/A

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

    6. lower-unsound-*.f64 N/A

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

    7. lower-unsound-+.f64 80.8%

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

13. Applied rewrites 80.8%

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

    1. lift--.f64 N/A

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

    2. flip-- N/A

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

    3. lower-unsound-/.f64 N/A

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

    4. lower-unsound--.f64 N/A

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

    5. lower-unsound-*.f64 N/A

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

    6. lower-unsound-*.f64 N/A

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

    7. lower-unsound-+.f64 80.8%

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

15. Applied rewrites 80.8%

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

    1. lift--.f64 N/A

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

    2. flip-- N/A

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

    3. lower-unsound-/.f64 N/A

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

    4. lower-unsound--.f64 N/A

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

    5. lower-unsound-*.f64 N/A

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

    6. lower-unsound-*.f64 N/A

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

    7. lower-unsound-+.f64 80.8%

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

17. Applied rewrites 80.8%

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

Alternative 2: 80.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{-3275911}{10000000} \cdot \left|x\right| - 1\\ t_1 := e^{x \cdot x}\\ t_2 := \frac{3275911}{10000000} \cdot \left|x\right| - -1\\ t_3 := \frac{\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{\frac{1061405429}{1000000000}}{t\_2} - \frac{1453152027}{1000000000}}{t\_2} - \frac{-1421413741}{1000000000}}{t\_0}}{t\_0}}{t\_1 \cdot t\_2}\\ \frac{{1}^{3} - \frac{1}{\frac{{\left(t\_1 \cdot \left(\left|x\right| \cdot \frac{3275911}{10000000} - -1\right)\right)}^{3}}{{\left(\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{1421413741}{1000000000} \cdot t\_2 - \left(\frac{\frac{-1061405429}{1000000000}}{t\_2} - \frac{-1453152027}{1000000000}\right)}{t\_2 \cdot t\_0}}{t\_0}\right)}^{3}}}}{1 + \left({t\_3}^{2} + 1 \cdot t\_3\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* -3275911/10000000 (fabs x)) 1))
       (t_1 (exp (* x x)))
       (t_2 (- (* 3275911/10000000 (fabs x)) -1))
       (t_3
        (/
         (-
          31853699/125000000
          (/
           (-
            -8890523/31250000
            (/
             (-
              (/
               (- (/ 1061405429/1000000000 t_2) 1453152027/1000000000)
               t_2)
              -1421413741/1000000000)
             t_0))
           t_0))
         (* t_1 t_2))))
  (/
   (-
    (pow 1 3)
    (/
     1
     (/
      (pow (* t_1 (- (* (fabs x) 3275911/10000000) -1)) 3)
      (pow
       (-
        31853699/125000000
        (/
         (-
          -8890523/31250000
          (/
           (-
            (* 1421413741/1000000000 t_2)
            (- (/ -1061405429/1000000000 t_2) -1453152027/1000000000))
           (* t_2 t_0)))
         t_0))
       3))))
   (+ 1 (+ (pow t_3 2) (* 1 t_3))))))

C

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

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 = ((-0.3275911d0) * abs(x)) - 1.0d0
    t_1 = exp((x * x))
    t_2 = (0.3275911d0 * abs(x)) - (-1.0d0)
    t_3 = (0.254829592d0 - (((-0.284496736d0) - (((((1.061405429d0 / t_2) - 1.453152027d0) / t_2) - (-1.421413741d0)) / t_0)) / t_0)) / (t_1 * t_2)
    code = ((1.0d0 ** 3.0d0) - (1.0d0 / (((t_1 * ((abs(x) * 0.3275911d0) - (-1.0d0))) ** 3.0d0) / ((0.254829592d0 - (((-0.284496736d0) - (((1.421413741d0 * t_2) - (((-1.061405429d0) / t_2) - (-1.453152027d0))) / (t_2 * t_0))) / t_0)) ** 3.0d0)))) / (1.0d0 + ((t_3 ** 2.0d0) + (1.0d0 * t_3)))
end function

Java

public static double code(double x) {
	double t_0 = (-0.3275911 * Math.abs(x)) - 1.0;
	double t_1 = Math.exp((x * x));
	double t_2 = (0.3275911 * Math.abs(x)) - -1.0;
	double t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_0)) / t_0)) / (t_1 * t_2);
	return (Math.pow(1.0, 3.0) - (1.0 / (Math.pow((t_1 * ((Math.abs(x) * 0.3275911) - -1.0)), 3.0) / Math.pow((0.254829592 - ((-0.284496736 - (((1.421413741 * t_2) - ((-1.061405429 / t_2) - -1.453152027)) / (t_2 * t_0))) / t_0)), 3.0)))) / (1.0 + (Math.pow(t_3, 2.0) + (1.0 * t_3)));
}

Python

def code(x):
	t_0 = (-0.3275911 * math.fabs(x)) - 1.0
	t_1 = math.exp((x * x))
	t_2 = (0.3275911 * math.fabs(x)) - -1.0
	t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_0)) / t_0)) / (t_1 * t_2)
	return (math.pow(1.0, 3.0) - (1.0 / (math.pow((t_1 * ((math.fabs(x) * 0.3275911) - -1.0)), 3.0) / math.pow((0.254829592 - ((-0.284496736 - (((1.421413741 * t_2) - ((-1.061405429 / t_2) - -1.453152027)) / (t_2 * t_0))) / t_0)), 3.0)))) / (1.0 + (math.pow(t_3, 2.0) + (1.0 * t_3)))

Julia

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

MATLAB

function tmp = code(x)
	t_0 = (-0.3275911 * abs(x)) - 1.0;
	t_1 = exp((x * x));
	t_2 = (0.3275911 * abs(x)) - -1.0;
	t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_2) - 1.453152027) / t_2) - -1.421413741) / t_0)) / t_0)) / (t_1 * t_2);
	tmp = ((1.0 ^ 3.0) - (1.0 / (((t_1 * ((abs(x) * 0.3275911) - -1.0)) ^ 3.0) / ((0.254829592 - ((-0.284496736 - (((1.421413741 * t_2) - ((-1.061405429 / t_2) - -1.453152027)) / (t_2 * t_0))) / t_0)) ^ 3.0)))) / (1.0 + ((t_3 ^ 2.0) + (1.0 * t_3)));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(N[(1061405429/1000000000 / t$95$2), $MachinePrecision] - 1453152027/1000000000), $MachinePrecision] / t$95$2), $MachinePrecision] - -1421413741/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[Power[1, 3], $MachinePrecision] - N[(1 / N[(N[Power[N[(t$95$1 * N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision] / N[Power[N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(1421413741/1000000000 * t$95$2), $MachinePrecision] - N[(N[(-1061405429/1000000000 / t$95$2), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision]), $MachinePrecision] / N[(t$95$2 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1 + N[(N[Power[t$95$3, 2], $MachinePrecision] + N[(1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 80.8%

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

9. Applied rewrites 80.8%

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

Alternative 3: 80.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{3275911}{10000000} \cdot \left|x\right| - -1\\ t_1 := \frac{-3275911}{10000000} \cdot \left|x\right|\\ t_2 := t\_1 - 1\\ t_3 := e^{x \cdot x}\\ t_4 := \frac{\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{\frac{1061405429}{1000000000}}{t\_0} - \frac{1453152027}{1000000000}}{t\_0} - \frac{-1421413741}{1000000000}}{t\_2}}{t\_2}}{t\_3 \cdot t\_0}\\ t_5 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_6 := -1 - t\_5\\ \frac{{1}^{3} - \frac{1}{\frac{{\left(t\_3 \cdot \left(t\_5 - -1\right)\right)}^{3}}{{\left(\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{t\_6}}{t\_6} - \frac{1421413741}{1000000000}}{1 - t\_1}}{t\_2}\right)}^{3}}}}{1 + \left({t\_4}^{2} + 1 \cdot t\_4\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* 3275911/10000000 (fabs x)) -1))
       (t_1 (* -3275911/10000000 (fabs x)))
       (t_2 (- t_1 1))
       (t_3 (exp (* x x)))
       (t_4
        (/
         (-
          31853699/125000000
          (/
           (-
            -8890523/31250000
            (/
             (-
              (/
               (- (/ 1061405429/1000000000 t_0) 1453152027/1000000000)
               t_0)
              -1421413741/1000000000)
             t_2))
           t_2))
         (* t_3 t_0)))
       (t_5 (* (fabs x) 3275911/10000000))
       (t_6 (- -1 t_5)))
  (/
   (-
    (pow 1 3)
    (/
     1
     (/
      (pow (* t_3 (- t_5 -1)) 3)
      (pow
       (-
        31853699/125000000
        (/
         (-
          -8890523/31250000
          (/
           (-
            (/
             (- -1453152027/1000000000 (/ 1061405429/1000000000 t_6))
             t_6)
            1421413741/1000000000)
           (- 1 t_1)))
         t_2))
       3))))
   (+ 1 (+ (pow t_4 2) (* 1 t_4))))))

C

double code(double x) {
	double t_0 = (0.3275911 * fabs(x)) - -1.0;
	double t_1 = -0.3275911 * fabs(x);
	double t_2 = t_1 - 1.0;
	double t_3 = exp((x * x));
	double t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_2)) / t_2)) / (t_3 * t_0);
	double t_5 = fabs(x) * 0.3275911;
	double t_6 = -1.0 - t_5;
	return (pow(1.0, 3.0) - (1.0 / (pow((t_3 * (t_5 - -1.0)), 3.0) / pow((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_1))) / t_2)), 3.0)))) / (1.0 + (pow(t_4, 2.0) + (1.0 * t_4)));
}

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
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    t_0 = (0.3275911d0 * abs(x)) - (-1.0d0)
    t_1 = (-0.3275911d0) * abs(x)
    t_2 = t_1 - 1.0d0
    t_3 = exp((x * x))
    t_4 = (0.254829592d0 - (((-0.284496736d0) - (((((1.061405429d0 / t_0) - 1.453152027d0) / t_0) - (-1.421413741d0)) / t_2)) / t_2)) / (t_3 * t_0)
    t_5 = abs(x) * 0.3275911d0
    t_6 = (-1.0d0) - t_5
    code = ((1.0d0 ** 3.0d0) - (1.0d0 / (((t_3 * (t_5 - (-1.0d0))) ** 3.0d0) / ((0.254829592d0 - (((-0.284496736d0) - (((((-1.453152027d0) - (1.061405429d0 / t_6)) / t_6) - 1.421413741d0) / (1.0d0 - t_1))) / t_2)) ** 3.0d0)))) / (1.0d0 + ((t_4 ** 2.0d0) + (1.0d0 * t_4)))
end function

Java

public static double code(double x) {
	double t_0 = (0.3275911 * Math.abs(x)) - -1.0;
	double t_1 = -0.3275911 * Math.abs(x);
	double t_2 = t_1 - 1.0;
	double t_3 = Math.exp((x * x));
	double t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_2)) / t_2)) / (t_3 * t_0);
	double t_5 = Math.abs(x) * 0.3275911;
	double t_6 = -1.0 - t_5;
	return (Math.pow(1.0, 3.0) - (1.0 / (Math.pow((t_3 * (t_5 - -1.0)), 3.0) / Math.pow((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_1))) / t_2)), 3.0)))) / (1.0 + (Math.pow(t_4, 2.0) + (1.0 * t_4)));
}

Python

def code(x):
	t_0 = (0.3275911 * math.fabs(x)) - -1.0
	t_1 = -0.3275911 * math.fabs(x)
	t_2 = t_1 - 1.0
	t_3 = math.exp((x * x))
	t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_2)) / t_2)) / (t_3 * t_0)
	t_5 = math.fabs(x) * 0.3275911
	t_6 = -1.0 - t_5
	return (math.pow(1.0, 3.0) - (1.0 / (math.pow((t_3 * (t_5 - -1.0)), 3.0) / math.pow((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_1))) / t_2)), 3.0)))) / (1.0 + (math.pow(t_4, 2.0) + (1.0 * t_4)))

Julia

function code(x)
	t_0 = Float64(Float64(0.3275911 * abs(x)) - -1.0)
	t_1 = Float64(-0.3275911 * abs(x))
	t_2 = Float64(t_1 - 1.0)
	t_3 = exp(Float64(x * x))
	t_4 = Float64(Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(Float64(1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_2)) / t_2)) / Float64(t_3 * t_0))
	t_5 = Float64(abs(x) * 0.3275911)
	t_6 = Float64(-1.0 - t_5)
	return Float64(Float64((1.0 ^ 3.0) - Float64(1.0 / Float64((Float64(t_3 * Float64(t_5 - -1.0)) ^ 3.0) / (Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(-1.453152027 - Float64(1.061405429 / t_6)) / t_6) - 1.421413741) / Float64(1.0 - t_1))) / t_2)) ^ 3.0)))) / Float64(1.0 + Float64((t_4 ^ 2.0) + Float64(1.0 * t_4))))
end

MATLAB

function tmp = code(x)
	t_0 = (0.3275911 * abs(x)) - -1.0;
	t_1 = -0.3275911 * abs(x);
	t_2 = t_1 - 1.0;
	t_3 = exp((x * x));
	t_4 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_2)) / t_2)) / (t_3 * t_0);
	t_5 = abs(x) * 0.3275911;
	t_6 = -1.0 - t_5;
	tmp = ((1.0 ^ 3.0) - (1.0 / (((t_3 * (t_5 - -1.0)) ^ 3.0) / ((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_6)) / t_6) - 1.421413741) / (1.0 - t_1))) / t_2)) ^ 3.0)))) / (1.0 + ((t_4 ^ 2.0) + (1.0 * t_4)));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$1 = N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - 1), $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(N[(1061405429/1000000000 / t$95$0), $MachinePrecision] - 1453152027/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - -1421413741/1000000000), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(t$95$3 * t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$6 = N[(-1 - t$95$5), $MachinePrecision]}, N[(N[(N[Power[1, 3], $MachinePrecision] - N[(1 / N[(N[Power[N[(t$95$3 * N[(t$95$5 - -1), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision] / N[Power[N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(-1453152027/1000000000 - N[(1061405429/1000000000 / t$95$6), $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / N[(1 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1 + N[(N[Power[t$95$4, 2], $MachinePrecision] + N[(1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 80.8%

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

Alternative 4: 79.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{-3275911}{10000000} \cdot \left|x\right|\\ t_1 := \frac{3275911}{10000000} \cdot \left|x\right| - -1\\ t_2 := t\_0 - 1\\ t_3 := \frac{\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{\frac{1061405429}{1000000000}}{t\_1} - \frac{1453152027}{1000000000}}{t\_1} - \frac{-1421413741}{1000000000}}{t\_2}}{t\_2}}{e^{x \cdot x} \cdot t\_1}\\ t_4 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_5 := -1 - t\_4\\ \frac{{1}^{3} - \frac{{\left(e^{\left(-x\right) \cdot x} \cdot \left(\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{t\_5}}{t\_5} - \frac{1421413741}{1000000000}}{1 - t\_0}}{t\_2}\right)\right)}^{3}}{{\left(t\_4 - -1\right)}^{3}}}{1 + \left({t\_3}^{2} + 1 \cdot t\_3\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* -3275911/10000000 (fabs x)))
       (t_1 (- (* 3275911/10000000 (fabs x)) -1))
       (t_2 (- t_0 1))
       (t_3
        (/
         (-
          31853699/125000000
          (/
           (-
            -8890523/31250000
            (/
             (-
              (/
               (- (/ 1061405429/1000000000 t_1) 1453152027/1000000000)
               t_1)
              -1421413741/1000000000)
             t_2))
           t_2))
         (* (exp (* x x)) t_1)))
       (t_4 (* (fabs x) 3275911/10000000))
       (t_5 (- -1 t_4)))
  (/
   (-
    (pow 1 3)
    (/
     (pow
      (*
       (exp (* (- x) x))
       (-
        31853699/125000000
        (/
         (-
          -8890523/31250000
          (/
           (-
            (/
             (- -1453152027/1000000000 (/ 1061405429/1000000000 t_5))
             t_5)
            1421413741/1000000000)
           (- 1 t_0)))
         t_2)))
      3)
     (pow (- t_4 -1) 3)))
   (+ 1 (+ (pow t_3 2) (* 1 t_3))))))

C

double code(double x) {
	double t_0 = -0.3275911 * fabs(x);
	double t_1 = (0.3275911 * fabs(x)) - -1.0;
	double t_2 = t_0 - 1.0;
	double t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_2)) / t_2)) / (exp((x * x)) * t_1);
	double t_4 = fabs(x) * 0.3275911;
	double t_5 = -1.0 - t_4;
	return (pow(1.0, 3.0) - (pow((exp((-x * x)) * (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_0))) / t_2))), 3.0) / pow((t_4 - -1.0), 3.0))) / (1.0 + (pow(t_3, 2.0) + (1.0 * t_3)));
}

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
    real(8) :: t_4
    real(8) :: t_5
    t_0 = (-0.3275911d0) * abs(x)
    t_1 = (0.3275911d0 * abs(x)) - (-1.0d0)
    t_2 = t_0 - 1.0d0
    t_3 = (0.254829592d0 - (((-0.284496736d0) - (((((1.061405429d0 / t_1) - 1.453152027d0) / t_1) - (-1.421413741d0)) / t_2)) / t_2)) / (exp((x * x)) * t_1)
    t_4 = abs(x) * 0.3275911d0
    t_5 = (-1.0d0) - t_4
    code = ((1.0d0 ** 3.0d0) - (((exp((-x * x)) * (0.254829592d0 - (((-0.284496736d0) - (((((-1.453152027d0) - (1.061405429d0 / t_5)) / t_5) - 1.421413741d0) / (1.0d0 - t_0))) / t_2))) ** 3.0d0) / ((t_4 - (-1.0d0)) ** 3.0d0))) / (1.0d0 + ((t_3 ** 2.0d0) + (1.0d0 * t_3)))
end function

Java

public static double code(double x) {
	double t_0 = -0.3275911 * Math.abs(x);
	double t_1 = (0.3275911 * Math.abs(x)) - -1.0;
	double t_2 = t_0 - 1.0;
	double t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_2)) / t_2)) / (Math.exp((x * x)) * t_1);
	double t_4 = Math.abs(x) * 0.3275911;
	double t_5 = -1.0 - t_4;
	return (Math.pow(1.0, 3.0) - (Math.pow((Math.exp((-x * x)) * (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_0))) / t_2))), 3.0) / Math.pow((t_4 - -1.0), 3.0))) / (1.0 + (Math.pow(t_3, 2.0) + (1.0 * t_3)));
}

Python

def code(x):
	t_0 = -0.3275911 * math.fabs(x)
	t_1 = (0.3275911 * math.fabs(x)) - -1.0
	t_2 = t_0 - 1.0
	t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_2)) / t_2)) / (math.exp((x * x)) * t_1)
	t_4 = math.fabs(x) * 0.3275911
	t_5 = -1.0 - t_4
	return (math.pow(1.0, 3.0) - (math.pow((math.exp((-x * x)) * (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_0))) / t_2))), 3.0) / math.pow((t_4 - -1.0), 3.0))) / (1.0 + (math.pow(t_3, 2.0) + (1.0 * t_3)))

Julia

function code(x)
	t_0 = Float64(-0.3275911 * abs(x))
	t_1 = Float64(Float64(0.3275911 * abs(x)) - -1.0)
	t_2 = Float64(t_0 - 1.0)
	t_3 = Float64(Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(Float64(1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_2)) / t_2)) / Float64(exp(Float64(x * x)) * t_1))
	t_4 = Float64(abs(x) * 0.3275911)
	t_5 = Float64(-1.0 - t_4)
	return Float64(Float64((1.0 ^ 3.0) - Float64((Float64(exp(Float64(Float64(-x) * x)) * Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(-1.453152027 - Float64(1.061405429 / t_5)) / t_5) - 1.421413741) / Float64(1.0 - t_0))) / t_2))) ^ 3.0) / (Float64(t_4 - -1.0) ^ 3.0))) / Float64(1.0 + Float64((t_3 ^ 2.0) + Float64(1.0 * t_3))))
end

MATLAB

function tmp = code(x)
	t_0 = -0.3275911 * abs(x);
	t_1 = (0.3275911 * abs(x)) - -1.0;
	t_2 = t_0 - 1.0;
	t_3 = (0.254829592 - ((-0.284496736 - (((((1.061405429 / t_1) - 1.453152027) / t_1) - -1.421413741) / t_2)) / t_2)) / (exp((x * x)) * t_1);
	t_4 = abs(x) * 0.3275911;
	t_5 = -1.0 - t_4;
	tmp = ((1.0 ^ 3.0) - (((exp((-x * x)) * (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_0))) / t_2))) ^ 3.0) / ((t_4 - -1.0) ^ 3.0))) / (1.0 + ((t_3 ^ 2.0) + (1.0 * t_3)));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - 1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(N[(1061405429/1000000000 / t$95$1), $MachinePrecision] - 1453152027/1000000000), $MachinePrecision] / t$95$1), $MachinePrecision] - -1421413741/1000000000), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$5 = N[(-1 - t$95$4), $MachinePrecision]}, N[(N[(N[Power[1, 3], $MachinePrecision] - N[(N[Power[N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(-1453152027/1000000000 - N[(1061405429/1000000000 / t$95$5), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / N[(1 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3], $MachinePrecision] / N[Power[N[(t$95$4 - -1), $MachinePrecision], 3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1 + N[(N[Power[t$95$3, 2], $MachinePrecision] + N[(1 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 79.7%

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

Alternative 5: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_1 := t\_0 - -1\\ t_2 := -1 - t\_0\\ t_3 := \frac{-3275911}{10000000} \cdot \left|x\right|\\ t_4 := t\_3 - 1\\ t_5 := \frac{\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{t\_2}}{t\_2} - \frac{1421413741}{1000000000}}{1 - t\_3}}{t\_4}}{e^{x \cdot x} \cdot t\_1}\\ \frac{\frac{1 - {t\_5}^{4}}{{t\_5}^{2} - -1}}{1 + \left(-\frac{\frac{\frac{\frac{\frac{\frac{-1061405429}{1000000000}}{t\_1} - \frac{-1453152027}{1000000000}}{t\_1} - \frac{1421413741}{1000000000}}{t\_1} - \frac{-8890523}{31250000}}{t\_4} - \frac{-31853699}{125000000}}{t\_4}\right) \cdot e^{\left(-x\right) \cdot x}} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* (fabs x) 3275911/10000000))
       (t_1 (- t_0 -1))
       (t_2 (- -1 t_0))
       (t_3 (* -3275911/10000000 (fabs x)))
       (t_4 (- t_3 1))
       (t_5
        (/
         (-
          31853699/125000000
          (/
           (-
            -8890523/31250000
            (/
             (-
              (/
               (-
                -1453152027/1000000000
                (/ 1061405429/1000000000 t_2))
               t_2)
              1421413741/1000000000)
             (- 1 t_3)))
           t_4))
         (* (exp (* x x)) t_1))))
  (/
   (/ (- 1 (pow t_5 4)) (- (pow t_5 2) -1))
   (+
    1
    (*
     (-
      (/
       (-
        (/
         (-
          (/
           (-
            (/
             (- (/ -1061405429/1000000000 t_1) -1453152027/1000000000)
             t_1)
            1421413741/1000000000)
           t_1)
          -8890523/31250000)
         t_4)
        -31853699/125000000)
       t_4))
     (exp (* (- x) x)))))))

C

double code(double x) {
	double t_0 = fabs(x) * 0.3275911;
	double t_1 = t_0 - -1.0;
	double t_2 = -1.0 - t_0;
	double t_3 = -0.3275911 * fabs(x);
	double t_4 = t_3 - 1.0;
	double t_5 = (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_2)) / t_2) - 1.421413741) / (1.0 - t_3))) / t_4)) / (exp((x * x)) * t_1);
	return ((1.0 - pow(t_5, 4.0)) / (pow(t_5, 2.0) - -1.0)) / (1.0 + (-(((((((((-1.061405429 / t_1) - -1.453152027) / t_1) - 1.421413741) / t_1) - -0.284496736) / t_4) - -0.254829592) / t_4) * exp((-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
    real(8) :: t_4
    real(8) :: t_5
    t_0 = abs(x) * 0.3275911d0
    t_1 = t_0 - (-1.0d0)
    t_2 = (-1.0d0) - t_0
    t_3 = (-0.3275911d0) * abs(x)
    t_4 = t_3 - 1.0d0
    t_5 = (0.254829592d0 - (((-0.284496736d0) - (((((-1.453152027d0) - (1.061405429d0 / t_2)) / t_2) - 1.421413741d0) / (1.0d0 - t_3))) / t_4)) / (exp((x * x)) * t_1)
    code = ((1.0d0 - (t_5 ** 4.0d0)) / ((t_5 ** 2.0d0) - (-1.0d0))) / (1.0d0 + (-((((((((((-1.061405429d0) / t_1) - (-1.453152027d0)) / t_1) - 1.421413741d0) / t_1) - (-0.284496736d0)) / t_4) - (-0.254829592d0)) / t_4) * exp((-x * x))))
end function

Java

public static double code(double x) {
	double t_0 = Math.abs(x) * 0.3275911;
	double t_1 = t_0 - -1.0;
	double t_2 = -1.0 - t_0;
	double t_3 = -0.3275911 * Math.abs(x);
	double t_4 = t_3 - 1.0;
	double t_5 = (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_2)) / t_2) - 1.421413741) / (1.0 - t_3))) / t_4)) / (Math.exp((x * x)) * t_1);
	return ((1.0 - Math.pow(t_5, 4.0)) / (Math.pow(t_5, 2.0) - -1.0)) / (1.0 + (-(((((((((-1.061405429 / t_1) - -1.453152027) / t_1) - 1.421413741) / t_1) - -0.284496736) / t_4) - -0.254829592) / t_4) * Math.exp((-x * x))));
}

Python

def code(x):
	t_0 = math.fabs(x) * 0.3275911
	t_1 = t_0 - -1.0
	t_2 = -1.0 - t_0
	t_3 = -0.3275911 * math.fabs(x)
	t_4 = t_3 - 1.0
	t_5 = (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_2)) / t_2) - 1.421413741) / (1.0 - t_3))) / t_4)) / (math.exp((x * x)) * t_1)
	return ((1.0 - math.pow(t_5, 4.0)) / (math.pow(t_5, 2.0) - -1.0)) / (1.0 + (-(((((((((-1.061405429 / t_1) - -1.453152027) / t_1) - 1.421413741) / t_1) - -0.284496736) / t_4) - -0.254829592) / t_4) * math.exp((-x * x))))

Julia

function code(x)
	t_0 = Float64(abs(x) * 0.3275911)
	t_1 = Float64(t_0 - -1.0)
	t_2 = Float64(-1.0 - t_0)
	t_3 = Float64(-0.3275911 * abs(x))
	t_4 = Float64(t_3 - 1.0)
	t_5 = Float64(Float64(0.254829592 - Float64(Float64(-0.284496736 - Float64(Float64(Float64(Float64(-1.453152027 - Float64(1.061405429 / t_2)) / t_2) - 1.421413741) / Float64(1.0 - t_3))) / t_4)) / Float64(exp(Float64(x * x)) * t_1))
	return Float64(Float64(Float64(1.0 - (t_5 ^ 4.0)) / Float64((t_5 ^ 2.0) - -1.0)) / Float64(1.0 + Float64(Float64(-Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(-1.061405429 / t_1) - -1.453152027) / t_1) - 1.421413741) / t_1) - -0.284496736) / t_4) - -0.254829592) / t_4)) * exp(Float64(Float64(-x) * x)))))
end

MATLAB

function tmp = code(x)
	t_0 = abs(x) * 0.3275911;
	t_1 = t_0 - -1.0;
	t_2 = -1.0 - t_0;
	t_3 = -0.3275911 * abs(x);
	t_4 = t_3 - 1.0;
	t_5 = (0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_2)) / t_2) - 1.421413741) / (1.0 - t_3))) / t_4)) / (exp((x * x)) * t_1);
	tmp = ((1.0 - (t_5 ^ 4.0)) / ((t_5 ^ 2.0) - -1.0)) / (1.0 + (-(((((((((-1.061405429 / t_1) - -1.453152027) / t_1) - 1.421413741) / t_1) - -0.284496736) / t_4) - -0.254829592) / t_4) * exp((-x * x))));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - -1), $MachinePrecision]}, Block[{t$95$2 = N[(-1 - t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - 1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(-1453152027/1000000000 - N[(1061405429/1000000000 / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / N[(1 - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision] / N[(N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1 - N[Power[t$95$5, 4], $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$5, 2], $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision] / N[(1 + N[((-N[(N[(N[(N[(N[(N[(N[(N[(N[(-1061405429/1000000000 / t$95$1), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision] / t$95$1), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / t$95$1), $MachinePrecision] - -8890523/31250000), $MachinePrecision] / t$95$4), $MachinePrecision] - -31853699/125000000), $MachinePrecision] / t$95$4), $MachinePrecision]) * N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 79.7%

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

Alternative 6: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_1 := t\_0 - -1\\ t_2 := \frac{-3275911}{10000000} \cdot \left|x\right| - 1\\ t_3 := \frac{\left(\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{1421413741}{1000000000} \cdot t\_1 - \left(\frac{\frac{1061405429}{1000000000}}{-1 - t\_0} - \frac{-1453152027}{1000000000}\right)}{t\_1}}{t\_2}}{t\_2}\right) \cdot e^{\left(-x\right) \cdot x}}{\frac{3275911}{10000000} \cdot \left|x\right| - -1}\\ \frac{1 \cdot 1 - t\_3 \cdot t\_3}{1 + t\_3} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* (fabs x) 3275911/10000000))
       (t_1 (- t_0 -1))
       (t_2 (- (* -3275911/10000000 (fabs x)) 1))
       (t_3
        (/
         (*
          (-
           31853699/125000000
           (/
            (-
             -8890523/31250000
             (/
              (/
               (-
                (* 1421413741/1000000000 t_1)
                (-
                 (/ 1061405429/1000000000 (- -1 t_0))
                 -1453152027/1000000000))
               t_1)
              t_2))
            t_2))
          (exp (* (- x) x)))
         (- (* 3275911/10000000 (fabs x)) -1))))
  (/ (- (* 1 1) (* t_3 t_3)) (+ 1 t_3))))

C

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

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 = abs(x) * 0.3275911d0
    t_1 = t_0 - (-1.0d0)
    t_2 = ((-0.3275911d0) * abs(x)) - 1.0d0
    t_3 = ((0.254829592d0 - (((-0.284496736d0) - ((((1.421413741d0 * t_1) - ((1.061405429d0 / ((-1.0d0) - t_0)) - (-1.453152027d0))) / t_1) / t_2)) / t_2)) * exp((-x * x))) / ((0.3275911d0 * abs(x)) - (-1.0d0))
    code = ((1.0d0 * 1.0d0) - (t_3 * t_3)) / (1.0d0 + t_3)
end function

Java

public static double code(double x) {
	double t_0 = Math.abs(x) * 0.3275911;
	double t_1 = t_0 - -1.0;
	double t_2 = (-0.3275911 * Math.abs(x)) - 1.0;
	double t_3 = ((0.254829592 - ((-0.284496736 - ((((1.421413741 * t_1) - ((1.061405429 / (-1.0 - t_0)) - -1.453152027)) / t_1) / t_2)) / t_2)) * Math.exp((-x * x))) / ((0.3275911 * Math.abs(x)) - -1.0);
	return ((1.0 * 1.0) - (t_3 * t_3)) / (1.0 + t_3);
}

Python

def code(x):
	t_0 = math.fabs(x) * 0.3275911
	t_1 = t_0 - -1.0
	t_2 = (-0.3275911 * math.fabs(x)) - 1.0
	t_3 = ((0.254829592 - ((-0.284496736 - ((((1.421413741 * t_1) - ((1.061405429 / (-1.0 - t_0)) - -1.453152027)) / t_1) / t_2)) / t_2)) * math.exp((-x * x))) / ((0.3275911 * math.fabs(x)) - -1.0)
	return ((1.0 * 1.0) - (t_3 * t_3)) / (1.0 + t_3)

Julia

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

MATLAB

function tmp = code(x)
	t_0 = abs(x) * 0.3275911;
	t_1 = t_0 - -1.0;
	t_2 = (-0.3275911 * abs(x)) - 1.0;
	t_3 = ((0.254829592 - ((-0.284496736 - ((((1.421413741 * t_1) - ((1.061405429 / (-1.0 - t_0)) - -1.453152027)) / t_1) / t_2)) / t_2)) * exp((-x * x))) / ((0.3275911 * abs(x)) - -1.0);
	tmp = ((1.0 * 1.0) - (t_3 * t_3)) / (1.0 + t_3);
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - -1), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(1421413741/1000000000 * t$95$1), $MachinePrecision] - N[(N[(1061405429/1000000000 / N[(-1 - t$95$0), $MachinePrecision]), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(1 * 1), $MachinePrecision] - N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision] / N[(1 + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 79.7%

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

9. Applied rewrites 79.7%

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

11. Applied rewrites 79.7%

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

13. Applied rewrites 79.7%

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

15. Applied rewrites 79.7%

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

Alternative 7: 79.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{3275911}{10000000} \cdot \left|x\right| - -1\\ t_1 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_2 := \frac{-3275911}{10000000} \cdot \left|x\right|\\ t_3 := t\_2 - 1\\ t_4 := \frac{\left(\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{\frac{1061405429}{1000000000}}{t\_0} - \frac{1453152027}{1000000000}}{t\_0} - \frac{-1421413741}{1000000000}}{t\_3}}{t\_3}\right) \cdot e^{\left(-x\right) \cdot x}}{t\_0}\\ t_5 := -1 - t\_1\\ \frac{1 \cdot 1 - t\_4 \cdot t\_4}{\frac{\frac{31853699}{125000000} - \frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{t\_5}}{t\_5} - \frac{1421413741}{1000000000}}{1 - t\_2}}{t\_3}}{e^{x \cdot x} \cdot \left(t\_1 - -1\right)} - -1} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* 3275911/10000000 (fabs x)) -1))
       (t_1 (* (fabs x) 3275911/10000000))
       (t_2 (* -3275911/10000000 (fabs x)))
       (t_3 (- t_2 1))
       (t_4
        (/
         (*
          (-
           31853699/125000000
           (/
            (-
             -8890523/31250000
             (/
              (-
               (/
                (-
                 (/ 1061405429/1000000000 t_0)
                 1453152027/1000000000)
                t_0)
               -1421413741/1000000000)
              t_3))
            t_3))
          (exp (* (- x) x)))
         t_0))
       (t_5 (- -1 t_1)))
  (/
   (- (* 1 1) (* t_4 t_4))
   (-
    (/
     (-
      31853699/125000000
      (/
       (-
        -8890523/31250000
        (/
         (-
          (/
           (- -1453152027/1000000000 (/ 1061405429/1000000000 t_5))
           t_5)
          1421413741/1000000000)
         (- 1 t_2)))
       t_3))
     (* (exp (* x x)) (- t_1 -1)))
    -1))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    t_0 = (0.3275911d0 * abs(x)) - (-1.0d0)
    t_1 = abs(x) * 0.3275911d0
    t_2 = (-0.3275911d0) * abs(x)
    t_3 = t_2 - 1.0d0
    t_4 = ((0.254829592d0 - (((-0.284496736d0) - (((((1.061405429d0 / t_0) - 1.453152027d0) / t_0) - (-1.421413741d0)) / t_3)) / t_3)) * exp((-x * x))) / t_0
    t_5 = (-1.0d0) - t_1
    code = ((1.0d0 * 1.0d0) - (t_4 * t_4)) / (((0.254829592d0 - (((-0.284496736d0) - (((((-1.453152027d0) - (1.061405429d0 / t_5)) / t_5) - 1.421413741d0) / (1.0d0 - t_2))) / t_3)) / (exp((x * x)) * (t_1 - (-1.0d0)))) - (-1.0d0))
end function

Java

public static double code(double x) {
	double t_0 = (0.3275911 * Math.abs(x)) - -1.0;
	double t_1 = Math.abs(x) * 0.3275911;
	double t_2 = -0.3275911 * Math.abs(x);
	double t_3 = t_2 - 1.0;
	double t_4 = ((0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_3)) / t_3)) * Math.exp((-x * x))) / t_0;
	double t_5 = -1.0 - t_1;
	return ((1.0 * 1.0) - (t_4 * t_4)) / (((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_2))) / t_3)) / (Math.exp((x * x)) * (t_1 - -1.0))) - -1.0);
}

Python

def code(x):
	t_0 = (0.3275911 * math.fabs(x)) - -1.0
	t_1 = math.fabs(x) * 0.3275911
	t_2 = -0.3275911 * math.fabs(x)
	t_3 = t_2 - 1.0
	t_4 = ((0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_3)) / t_3)) * math.exp((-x * x))) / t_0
	t_5 = -1.0 - t_1
	return ((1.0 * 1.0) - (t_4 * t_4)) / (((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_2))) / t_3)) / (math.exp((x * x)) * (t_1 - -1.0))) - -1.0)

Julia

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

MATLAB

function tmp = code(x)
	t_0 = (0.3275911 * abs(x)) - -1.0;
	t_1 = abs(x) * 0.3275911;
	t_2 = -0.3275911 * abs(x);
	t_3 = t_2 - 1.0;
	t_4 = ((0.254829592 - ((-0.284496736 - (((((1.061405429 / t_0) - 1.453152027) / t_0) - -1.421413741) / t_3)) / t_3)) * exp((-x * x))) / t_0;
	t_5 = -1.0 - t_1;
	tmp = ((1.0 * 1.0) - (t_4 * t_4)) / (((0.254829592 - ((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_5)) / t_5) - 1.421413741) / (1.0 - t_2))) / t_3)) / (exp((x * x)) * (t_1 - -1.0))) - -1.0);
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$2 = N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - 1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(N[(1061405429/1000000000 / t$95$0), $MachinePrecision] - 1453152027/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - -1421413741/1000000000), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] * N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(-1 - t$95$1), $MachinePrecision]}, N[(N[(N[(1 * 1), $MachinePrecision] - N[(t$95$4 * t$95$4), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(31853699/125000000 - N[(N[(-8890523/31250000 - N[(N[(N[(N[(-1453152027/1000000000 - N[(1061405429/1000000000 / t$95$5), $MachinePrecision]), $MachinePrecision] / t$95$5), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / N[(1 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 - -1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

7. Applied rewrites 79.7%

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

9. Applied rewrites 79.7%

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

11. Applied rewrites 79.7%

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

Alternative 8: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000} - -1\\ t_1 := \frac{3275911}{10000000} \cdot \left|x\right| - -1\\ 1 - \frac{\frac{\frac{\frac{\frac{-1421413741}{1000000000} \cdot t\_1 - \frac{\frac{-1453152027}{1000000000} \cdot t\_0 - \frac{-1061405429}{1000000000}}{t\_0}}{t\_1}}{t\_0} - \frac{-8890523}{31250000}}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - \frac{-31853699}{125000000}}{t\_0 \cdot e^{x \cdot x}} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* (fabs x) 3275911/10000000) -1))
       (t_1 (- (* 3275911/10000000 (fabs x)) -1)))
  (-
   1
   (/
    (-
     (/
      (-
       (/
        (/
         (-
          (* -1421413741/1000000000 t_1)
          (/
           (- (* -1453152027/1000000000 t_0) -1061405429/1000000000)
           t_0))
         t_1)
        t_0)
       -8890523/31250000)
      (- (* -3275911/10000000 (fabs x)) 1))
     -31853699/125000000)
    (* t_0 (exp (* x x)))))))

C

double code(double x) {
	double t_0 = (fabs(x) * 0.3275911) - -1.0;
	double t_1 = (0.3275911 * fabs(x)) - -1.0;
	return 1.0 - ((((((((-1.421413741 * t_1) - (((-1.453152027 * t_0) - -1.061405429) / t_0)) / t_1) / t_0) - -0.284496736) / ((-0.3275911 * fabs(x)) - 1.0)) - -0.254829592) / (t_0 * exp((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
    t_0 = (abs(x) * 0.3275911d0) - (-1.0d0)
    t_1 = (0.3275911d0 * abs(x)) - (-1.0d0)
    code = 1.0d0 - (((((((((-1.421413741d0) * t_1) - ((((-1.453152027d0) * t_0) - (-1.061405429d0)) / t_0)) / t_1) / t_0) - (-0.284496736d0)) / (((-0.3275911d0) * abs(x)) - 1.0d0)) - (-0.254829592d0)) / (t_0 * exp((x * x))))
end function

Java

public static double code(double x) {
	double t_0 = (Math.abs(x) * 0.3275911) - -1.0;
	double t_1 = (0.3275911 * Math.abs(x)) - -1.0;
	return 1.0 - ((((((((-1.421413741 * t_1) - (((-1.453152027 * t_0) - -1.061405429) / t_0)) / t_1) / t_0) - -0.284496736) / ((-0.3275911 * Math.abs(x)) - 1.0)) - -0.254829592) / (t_0 * Math.exp((x * x))));
}

Python

def code(x):
	t_0 = (math.fabs(x) * 0.3275911) - -1.0
	t_1 = (0.3275911 * math.fabs(x)) - -1.0
	return 1.0 - ((((((((-1.421413741 * t_1) - (((-1.453152027 * t_0) - -1.061405429) / t_0)) / t_1) / t_0) - -0.284496736) / ((-0.3275911 * math.fabs(x)) - 1.0)) - -0.254829592) / (t_0 * math.exp((x * x))))

Julia

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

MATLAB

function tmp = code(x)
	t_0 = (abs(x) * 0.3275911) - -1.0;
	t_1 = (0.3275911 * abs(x)) - -1.0;
	tmp = 1.0 - ((((((((-1.421413741 * t_1) - (((-1.453152027 * t_0) - -1.061405429) / t_0)) / t_1) / t_0) - -0.284496736) / ((-0.3275911 * abs(x)) - 1.0)) - -0.254829592) / (t_0 * exp((x * x))));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - -1), $MachinePrecision]}, N[(1 - N[(N[(N[(N[(N[(N[(N[(N[(-1421413741/1000000000 * t$95$1), $MachinePrecision] - N[(N[(N[(-1453152027/1000000000 * t$95$0), $MachinePrecision] - -1061405429/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] / t$95$0), $MachinePrecision] - -8890523/31250000), $MachinePrecision] / N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision] / N[(t$95$0 * N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

5. Applied rewrites 79.7%

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

   1. lift--.f64 N/A

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

   2. sub-flip N/A

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

   3. lift-/.f64 N/A

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

   4. metadata-eval N/A

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

   5. distribute-frac-neg N/A

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

   6. lower-/.f64 N/A

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

   7. lift--.f64 N/A

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

   8. sub-flip N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. sub-flip N/A

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

   13. lift--.f64 N/A

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

   14. distribute-neg-in N/A

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

   15. metadata-eval N/A

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

   16. sub-flip N/A

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

   17. lift--.f64 N/A

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

   18. lift--.f64 N/A

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

   19. sub-negate-rev N/A

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

7. Applied rewrites 79.7%

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

Alternative 9: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000} - -1\\ t_1 := 2 \cdot t\_0\\ \frac{t\_1 - 2 \cdot \left(e^{\left(-x\right) \cdot x} \cdot \left(\frac{\frac{\frac{\frac{\frac{-1061405429}{1000000000}}{t\_0} - \frac{-1453152027}{1000000000}}{t\_0} - \frac{1421413741}{1000000000}}{t\_0} - \frac{-8890523}{31250000}}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - \frac{-31853699}{125000000}\right)\right)}{t\_1} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* (fabs x) 3275911/10000000) -1)) (t_1 (* 2 t_0)))
  (/
   (-
    t_1
    (*
     2
     (*
      (exp (* (- x) x))
      (-
       (/
        (-
         (/
          (-
           (/
            (- (/ -1061405429/1000000000 t_0) -1453152027/1000000000)
            t_0)
           1421413741/1000000000)
          t_0)
         -8890523/31250000)
        (- (* -3275911/10000000 (fabs x)) 1))
       -31853699/125000000))))
   t_1)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    t_0 = (abs(x) * 0.3275911d0) - (-1.0d0)
    t_1 = 2.0d0 * t_0
    code = (t_1 - (2.0d0 * (exp((-x * x)) * (((((((((-1.061405429d0) / t_0) - (-1.453152027d0)) / t_0) - 1.421413741d0) / t_0) - (-0.284496736d0)) / (((-0.3275911d0) * abs(x)) - 1.0d0)) - (-0.254829592d0))))) / t_1
end function

Java

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

Python

def code(x):
	t_0 = (math.fabs(x) * 0.3275911) - -1.0
	t_1 = 2.0 * t_0
	return (t_1 - (2.0 * (math.exp((-x * x)) * ((((((((-1.061405429 / t_0) - -1.453152027) / t_0) - 1.421413741) / t_0) - -0.284496736) / ((-0.3275911 * math.fabs(x)) - 1.0)) - -0.254829592)))) / t_1

Julia

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

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision]}, Block[{t$95$1 = N[(2 * t$95$0), $MachinePrecision]}, N[(N[(t$95$1 - N[(2 * N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(-1061405429/1000000000 / t$95$0), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - -8890523/31250000), $MachinePrecision] / N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

Alternative 10: 79.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000} - -1\\ 1 - \frac{e^{\left(-x\right) \cdot x} \cdot \left(\frac{\frac{\frac{\frac{\frac{-1061405429}{1000000000}}{t\_0} - \frac{-1453152027}{1000000000}}{t\_0} - \frac{1421413741}{1000000000}}{t\_0} - \frac{-8890523}{31250000}}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - \frac{-31853699}{125000000}\right)}{t\_0} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* (fabs x) 3275911/10000000) -1)))
  (-
   1
   (/
    (*
     (exp (* (- x) x))
     (-
      (/
       (-
        (/
         (-
          (/
           (- (/ -1061405429/1000000000 t_0) -1453152027/1000000000)
           t_0)
          1421413741/1000000000)
         t_0)
        -8890523/31250000)
       (- (* -3275911/10000000 (fabs x)) 1))
      -31853699/125000000))
    t_0))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision]}, N[(1 - N[(N[(N[Exp[N[((-x) * x), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(-1061405429/1000000000 / t$95$0), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - -8890523/31250000), $MachinePrecision] / N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

Alternative 11: 79.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000} - -1\\ 1 - \frac{\frac{\frac{\frac{\frac{\frac{-1061405429}{1000000000}}{t\_0} - \frac{-1453152027}{1000000000}}{t\_0} - \frac{1421413741}{1000000000}}{t\_0} - \frac{-8890523}{31250000}}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - \frac{-31853699}{125000000}}{t\_0 \cdot e^{x \cdot x}} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* (fabs x) 3275911/10000000) -1)))
  (-
   1
   (/
    (-
     (/
      (-
       (/
        (-
         (/
          (- (/ -1061405429/1000000000 t_0) -1453152027/1000000000)
          t_0)
         1421413741/1000000000)
        t_0)
       -8890523/31250000)
      (- (* -3275911/10000000 (fabs x)) 1))
     -31853699/125000000)
    (* t_0 (exp (* x x)))))))

C

double code(double x) {
	double t_0 = (fabs(x) * 0.3275911) - -1.0;
	return 1.0 - (((((((((-1.061405429 / t_0) - -1.453152027) / t_0) - 1.421413741) / t_0) - -0.284496736) / ((-0.3275911 * fabs(x)) - 1.0)) - -0.254829592) / (t_0 * exp((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
    t_0 = (abs(x) * 0.3275911d0) - (-1.0d0)
    code = 1.0d0 - ((((((((((-1.061405429d0) / t_0) - (-1.453152027d0)) / t_0) - 1.421413741d0) / t_0) - (-0.284496736d0)) / (((-0.3275911d0) * abs(x)) - 1.0d0)) - (-0.254829592d0)) / (t_0 * exp((x * x))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision]}, N[(1 - N[(N[(N[(N[(N[(N[(N[(N[(N[(-1061405429/1000000000 / t$95$0), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - -8890523/31250000), $MachinePrecision] / N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision] / N[(t$95$0 * N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

Alternative 12: 79.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_0 := \frac{3275911}{10000000} \cdot \left|x\right|\\ t_1 := t\_0 - -1\\ 1 - \frac{\left(\frac{\frac{1421413741}{1000000000} - \frac{\frac{\frac{-1061405429}{1000000000}}{t\_1} - \frac{-1453152027}{1000000000}}{t\_1}}{-1 - t\_0} - \frac{-8890523}{31250000}\right) \cdot \frac{-1}{1 - \frac{-3275911}{10000000} \cdot \left|x\right|} - \frac{-31853699}{125000000}}{\left(\left|x\right| \cdot \frac{3275911}{10000000} - -1\right) \cdot \left(x \cdot x - -1\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* 3275911/10000000 (fabs x))) (t_1 (- t_0 -1)))
  (-
   1
   (/
    (-
     (*
      (-
       (/
        (-
         1421413741/1000000000
         (/
          (- (/ -1061405429/1000000000 t_1) -1453152027/1000000000)
          t_1))
        (- -1 t_0))
       -8890523/31250000)
      (/ -1 (- 1 (* -3275911/10000000 (fabs x)))))
     -31853699/125000000)
    (* (- (* (fabs x) 3275911/10000000) -1) (- (* x x) -1))))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    t_0 = 0.3275911d0 * abs(x)
    t_1 = t_0 - (-1.0d0)
    code = 1.0d0 - ((((((1.421413741d0 - ((((-1.061405429d0) / t_1) - (-1.453152027d0)) / t_1)) / ((-1.0d0) - t_0)) - (-0.284496736d0)) * ((-1.0d0) / (1.0d0 - ((-0.3275911d0) * abs(x))))) - (-0.254829592d0)) / (((abs(x) * 0.3275911d0) - (-1.0d0)) * ((x * x) - (-1.0d0))))
end function

Java

public static double code(double x) {
	double t_0 = 0.3275911 * Math.abs(x);
	double t_1 = t_0 - -1.0;
	return 1.0 - ((((((1.421413741 - (((-1.061405429 / t_1) - -1.453152027) / t_1)) / (-1.0 - t_0)) - -0.284496736) * (-1.0 / (1.0 - (-0.3275911 * Math.abs(x))))) - -0.254829592) / (((Math.abs(x) * 0.3275911) - -1.0) * ((x * x) - -1.0)));
}

Python

def code(x):
	t_0 = 0.3275911 * math.fabs(x)
	t_1 = t_0 - -1.0
	return 1.0 - ((((((1.421413741 - (((-1.061405429 / t_1) - -1.453152027) / t_1)) / (-1.0 - t_0)) - -0.284496736) * (-1.0 / (1.0 - (-0.3275911 * math.fabs(x))))) - -0.254829592) / (((math.fabs(x) * 0.3275911) - -1.0) * ((x * x) - -1.0)))

Julia

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

MATLAB

function tmp = code(x)
	t_0 = 0.3275911 * abs(x);
	t_1 = t_0 - -1.0;
	tmp = 1.0 - ((((((1.421413741 - (((-1.061405429 / t_1) - -1.453152027) / t_1)) / (-1.0 - t_0)) - -0.284496736) * (-1.0 / (1.0 - (-0.3275911 * abs(x))))) - -0.254829592) / (((abs(x) * 0.3275911) - -1.0) * ((x * x) - -1.0)));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - -1), $MachinePrecision]}, N[(1 - N[(N[(N[(N[(N[(N[(1421413741/1000000000 - N[(N[(N[(-1061405429/1000000000 / t$95$1), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(-1 - t$95$0), $MachinePrecision]), $MachinePrecision] - -8890523/31250000), $MachinePrecision] * N[(-1 / N[(1 - N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision] / N[(N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision] * N[(N[(x * x), $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

4. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-pow.f64 79.0%

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

6. Applied rewrites 79.0%

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

   1. lift-+.f64 N/A

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

   2. lift-pow.f64 N/A

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

   3. pow2 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. add-flip N/A

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

   7. metadata-eval N/A

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

   8. lower--.f64 79.0%

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

8. Applied rewrites 79.0%

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

10. Applied rewrites 79.0%

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

Alternative 13: 79.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000}\\ t_1 := -1 - t\_0\\ 1 - \left(\frac{\frac{-8890523}{31250000} - \frac{\frac{\frac{-1453152027}{1000000000} - \frac{\frac{1061405429}{1000000000}}{t\_1}}{t\_1} - \frac{1421413741}{1000000000}}{t\_0 - -1}}{1 - \frac{-3275911}{10000000} \cdot \left|x\right|} - \frac{-31853699}{125000000}\right) \cdot \frac{-1}{t\_1 \cdot \left(x \cdot x - -1\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* (fabs x) 3275911/10000000)) (t_1 (- -1 t_0)))
  (-
   1
   (*
    (-
     (/
      (-
       -8890523/31250000
       (/
        (-
         (/
          (- -1453152027/1000000000 (/ 1061405429/1000000000 t_1))
          t_1)
         1421413741/1000000000)
        (- t_0 -1)))
      (- 1 (* -3275911/10000000 (fabs x))))
     -31853699/125000000)
    (/ -1 (* t_1 (- (* x x) -1)))))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    t_0 = abs(x) * 0.3275911d0
    t_1 = (-1.0d0) - t_0
    code = 1.0d0 - (((((-0.284496736d0) - (((((-1.453152027d0) - (1.061405429d0 / t_1)) / t_1) - 1.421413741d0) / (t_0 - (-1.0d0)))) / (1.0d0 - ((-0.3275911d0) * abs(x)))) - (-0.254829592d0)) * ((-1.0d0) / (t_1 * ((x * x) - (-1.0d0)))))
end function

Java

public static double code(double x) {
	double t_0 = Math.abs(x) * 0.3275911;
	double t_1 = -1.0 - t_0;
	return 1.0 - ((((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_1)) / t_1) - 1.421413741) / (t_0 - -1.0))) / (1.0 - (-0.3275911 * Math.abs(x)))) - -0.254829592) * (-1.0 / (t_1 * ((x * x) - -1.0))));
}

Python

def code(x):
	t_0 = math.fabs(x) * 0.3275911
	t_1 = -1.0 - t_0
	return 1.0 - ((((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_1)) / t_1) - 1.421413741) / (t_0 - -1.0))) / (1.0 - (-0.3275911 * math.fabs(x)))) - -0.254829592) * (-1.0 / (t_1 * ((x * x) - -1.0))))

Julia

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

MATLAB

function tmp = code(x)
	t_0 = abs(x) * 0.3275911;
	t_1 = -1.0 - t_0;
	tmp = 1.0 - ((((-0.284496736 - ((((-1.453152027 - (1.061405429 / t_1)) / t_1) - 1.421413741) / (t_0 - -1.0))) / (1.0 - (-0.3275911 * abs(x)))) - -0.254829592) * (-1.0 / (t_1 * ((x * x) - -1.0))));
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision]}, Block[{t$95$1 = N[(-1 - t$95$0), $MachinePrecision]}, N[(1 - N[(N[(N[(N[(-8890523/31250000 - N[(N[(N[(N[(-1453152027/1000000000 - N[(1061405429/1000000000 / t$95$1), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / N[(t$95$0 - -1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1 - N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision] * N[(-1 / N[(t$95$1 * N[(N[(x * x), $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

4. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-pow.f64 79.0%

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

6. Applied rewrites 79.0%

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

8. Applied rewrites 79.0%

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

Alternative 14: 79.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_0 := \left|x\right| \cdot \frac{3275911}{10000000} - -1\\ 1 - \frac{\frac{\frac{\frac{\frac{\frac{-1061405429}{1000000000}}{t\_0} - \frac{-1453152027}{1000000000}}{t\_0} - \frac{1421413741}{1000000000}}{t\_0} - \frac{-8890523}{31250000}}{\frac{-3275911}{10000000} \cdot \left|x\right| - 1} - \frac{-31853699}{125000000}}{t\_0 \cdot \left(x \cdot x - -1\right)} \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (- (* (fabs x) 3275911/10000000) -1)))
  (-
   1
   (/
    (-
     (/
      (-
       (/
        (-
         (/
          (- (/ -1061405429/1000000000 t_0) -1453152027/1000000000)
          t_0)
         1421413741/1000000000)
        t_0)
       -8890523/31250000)
      (- (* -3275911/10000000 (fabs x)) 1))
     -31853699/125000000)
    (* t_0 (- (* x x) -1))))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[Abs[x], $MachinePrecision] * 3275911/10000000), $MachinePrecision] - -1), $MachinePrecision]}, N[(1 - N[(N[(N[(N[(N[(N[(N[(N[(N[(-1061405429/1000000000 / t$95$0), $MachinePrecision] - -1453152027/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - 1421413741/1000000000), $MachinePrecision] / t$95$0), $MachinePrecision] - -8890523/31250000), $MachinePrecision] / N[(N[(-3275911/10000000 * N[Abs[x], $MachinePrecision]), $MachinePrecision] - 1), $MachinePrecision]), $MachinePrecision] - -31853699/125000000), $MachinePrecision] / N[(t$95$0 * N[(N[(x * x), $MachinePrecision] - -1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.7%

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

3. Applied rewrites 79.7%

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

4. Taylor expanded in x around 0

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

   1. lower-+.f64 N/A

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

   2. lower-pow.f64 79.0%

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

6. Applied rewrites 79.0%

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

   1. lift-+.f64 N/A

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

   2. lift-pow.f64 N/A

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

   3. pow2 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. add-flip N/A

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

   7. metadata-eval N/A

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

   8. lower--.f64 79.0%

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

8. Applied rewrites 79.0%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ 31853699/125000000 (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ -8890523/31250000 (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ 1421413741/1000000000 (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) (+ -1453152027/1000000000 (* (/ 1 (+ 1 (* 3275911/10000000 (fabs x)))) 1061405429/1000000000))))))))) (exp (- (* (fabs x) (fabs x)))))))