(x - 1) to (x - 20)

Percentage Accurate: 97.8% → 97.8%

Time: 17.7s

Alternatives: 44

Speedup: 1.0×

Specification

\[1 \leq x \land x \leq 20\]

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                 (- x 5.0))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                 (- x 5.0))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 2\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (- x 2.0) (* (- x 3.0) (* (- x 4.0) (- x 5.0)))) (- x 1.0))
              (- x 7.0))
             (- x 10.0))
            (* (- x 6.0) (* (- x 8.0) (- x 9.0))))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((x - 2.0) * ((x - 3.0) * ((x - 4.0) * (x - 5.0)))) * (x - 1.0)) * (x - 7.0)) * (x - 10.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((x - 2.0d0) * ((x - 3.0d0) * ((x - 4.0d0) * (x - 5.0d0)))) * (x - 1.0d0)) * (x - 7.0d0)) * (x - 10.0d0)) * ((x - 6.0d0) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((x - 2.0) * ((x - 3.0) * ((x - 4.0) * (x - 5.0)))) * (x - 1.0)) * (x - 7.0)) * (x - 10.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((x - 2.0) * ((x - 3.0) * ((x - 4.0) * (x - 5.0)))) * (x - 1.0)) * (x - 7.0)) * (x - 10.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 2.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0)))) * Float64(x - 1.0)) * Float64(x - 7.0)) * Float64(x - 10.0)) * Float64(Float64(x - 6.0) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((x - 2.0) * ((x - 3.0) * ((x - 4.0) * (x - 5.0)))) * (x - 1.0)) * (x - 7.0)) * (x - 10.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. associate-*l* N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

7. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right)} \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \color{blue}{\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)}\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

9. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(x - 2\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
10. Add Preprocessing

Alternative 2: 97.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (- x 5.0) (- x 4.0))
                 (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((((x - 5.0) * (x - 4.0)) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((((x - 5.0d0) * (x - 4.0d0)) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((((x - 5.0) * (x - 4.0)) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((((x - 5.0) * (x - 4.0)) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 5.0) * Float64(x - 4.0)) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((((x - 5.0) * (x - 4.0)) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Add Preprocessing

Alternative 3: 97.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 2\right) \cdot \left(\left(x - 1\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 3\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (- x 2.0) (* (- x 1.0) (* (- x 4.0) (- x 3.0))))
                 (- x 5.0))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((((x - 2.0) * ((x - 1.0) * ((x - 4.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((((x - 2.0d0) * ((x - 1.0d0) * ((x - 4.0d0) * (x - 3.0d0)))) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((((x - 2.0) * ((x - 1.0) * ((x - 4.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((((x - 2.0) * ((x - 1.0) * ((x - 4.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 2.0) * Float64(Float64(x - 1.0) * Float64(Float64(x - 4.0) * Float64(x - 3.0)))) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((((x - 2.0) * ((x - 1.0) * ((x - 4.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)} \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(x - 4\right)\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)} \cdot \left(\left(x - 3\right) \cdot \left(x - 4\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)} \cdot \left(\left(x - 3\right) \cdot \left(x - 4\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 2\right) \cdot \left(\left(x - 1\right) \cdot \left(\left(x - 3\right) \cdot \left(x - 4\right)\right)\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 2\right) \cdot \left(\left(x - 1\right) \cdot \left(\left(x - 3\right) \cdot \left(x - 4\right)\right)\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 2\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(\left(x - 3\right) \cdot \left(x - 4\right)\right)\right)}\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 2\right) \cdot \left(\left(x - 1\right) \cdot \color{blue}{\left(\left(x - 4\right) \cdot \left(x - 3\right)\right)}\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 2\right) \cdot \left(\left(x - 1\right) \cdot \color{blue}{\left(\left(x - 4\right) \cdot \left(x - 3\right)\right)}\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 2\right) \cdot \left(\left(x - 1\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 3\right)\right)\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Add Preprocessing

Alternative 4: 97.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (- x 3.0) (* (- x 4.0) (- x 5.0))) (- x 2.0))
                 (- x 1.0))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 2.0)) * (x - 1.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = ((((((((((((((((((x - 3.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * (x - 2.0d0)) * (x - 1.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 2.0)) * (x - 1.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 2.0)) * (x - 1.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(x - 2.0)) * Float64(x - 1.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 2.0)) * (x - 1.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right)} \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)} \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)} \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)}\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 4\right) \cdot \left(x - 5\right)\right)}\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 4\right) \cdot \left(x - 5\right)\right)}\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
6. Add Preprocessing

Alternative 5: 97.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (- x 3.0) (* (- x 4.0) (- x 5.0))) (- x 1.0))
                 (- x 2.0))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 1.0)) * (x - 2.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = ((((((((((((((((((x - 3.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * (x - 1.0d0)) * (x - 2.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 1.0)) * (x - 2.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 1.0)) * (x - 2.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(x - 1.0)) * Float64(x - 2.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = ((((((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (x - 1.0)) * (x - 2.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 1\right)\right)} \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)} \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)} \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)}\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 4\right) \cdot \left(x - 5\right)\right)}\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 4\right) \cdot \left(x - 5\right)\right)}\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
6. Add Preprocessing

Alternative 6: 23.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 9.2:\\ \;\;\;\;\left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(380 + -39 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot 42\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 9.2)
   (*
    (*
     (- x 18.0)
     (*
      (*
       (*
        (*
         (- x 11.0)
         (*
          (- x 10.0)
          (*
           (- x 9.0)
           (*
            (*
             (- x 8.0)
             (*
              (* (* (* (* (- x 5.0) (- x 4.0)) (- x 3.0)) (- x 2.0)) (- x 1.0))
              (- x 6.0)))
            (- x 7.0)))))
        (* (- x 13.0) (- x 12.0)))
       (* (- x 15.0) (- x 14.0)))
      (* (- x 17.0) (- x 16.0))))
    (+ 380.0 (* -39.0 x)))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (- x 3.0) (* (- x 4.0) (- x 5.0)))
                 (* (* (- x 1.0) (- x 2.0)) 42.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 9.2) {
		tmp = ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * (380.0 + (-39.0 * x));
	} else {
		tmp = (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 9.2d0) then
        tmp = ((x - 18.0d0) * (((((x - 11.0d0) * ((x - 10.0d0) * ((x - 9.0d0) * (((x - 8.0d0) * ((((((x - 5.0d0) * (x - 4.0d0)) * (x - 3.0d0)) * (x - 2.0d0)) * (x - 1.0d0)) * (x - 6.0d0))) * (x - 7.0d0))))) * ((x - 13.0d0) * (x - 12.0d0))) * ((x - 15.0d0) * (x - 14.0d0))) * ((x - 17.0d0) * (x - 16.0d0)))) * (380.0d0 + ((-39.0d0) * x))
    else
        tmp = (((((((((((((((x - 3.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * (((x - 1.0d0) * (x - 2.0d0)) * 42.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 9.2) {
		tmp = ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * (380.0 + (-39.0 * x));
	} else {
		tmp = (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 9.2:
		tmp = ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * (380.0 + (-39.0 * x))
	else:
		tmp = (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 9.2)
		tmp = Float64(Float64(Float64(x - 18.0) * Float64(Float64(Float64(Float64(Float64(x - 11.0) * Float64(Float64(x - 10.0) * Float64(Float64(x - 9.0) * Float64(Float64(Float64(x - 8.0) * Float64(Float64(Float64(Float64(Float64(Float64(x - 5.0) * Float64(x - 4.0)) * Float64(x - 3.0)) * Float64(x - 2.0)) * Float64(x - 1.0)) * Float64(x - 6.0))) * Float64(x - 7.0))))) * Float64(Float64(x - 13.0) * Float64(x - 12.0))) * Float64(Float64(x - 15.0) * Float64(x - 14.0))) * Float64(Float64(x - 17.0) * Float64(x - 16.0)))) * Float64(380.0 + Float64(-39.0 * x)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * 42.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 9.2)
		tmp = ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * (380.0 + (-39.0 * x));
	else
		tmp = (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 9.2], N[(N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 11.0), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(380.0 + N[(-39.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * 42.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.1999999999999993

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 97.8%

      \[\leadsto \color{blue}{\left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \color{blue}{\left(380 + -39 \cdot x\right)} \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(380 + \color{blue}{-39 \cdot x}\right) \]

      2. lower-*.f64 19.4%

         \[\leadsto \left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(380 + -39 \cdot \color{blue}{x}\right) \]

   10. Applied rewrites 19.4%

       \[\leadsto \left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \color{blue}{\left(380 + -39 \cdot x\right)} \]

   if 9.1999999999999993 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \color{blue}{42}\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 17.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \color{blue}{42}\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 20.8% accurate, 1.0× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                 (- x 5.0))
                (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  -20.0))

C

double code(double x) {
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (-20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
}

Python

def code(x):
	return (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * -20.0)
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * -20.0), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

2. Taylor expanded in x around 0

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \color{blue}{-20} \]
3. Step-by-step derivation

4. Applied rewrites 20.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \color{blue}{-20} \]
5. Add Preprocessing

Alternative 8: 19.1% accurate, 1.1× speedup

Math

\[\left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot 380 \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (- x 18.0)
   (*
    (*
     (*
      (*
       (- x 11.0)
       (*
        (- x 10.0)
        (*
         (- x 9.0)
         (*
          (*
           (- x 8.0)
           (*
            (* (* (* (* (- x 5.0) (- x 4.0)) (- x 3.0)) (- x 2.0)) (- x 1.0))
            (- x 6.0)))
          (- x 7.0)))))
      (* (- x 13.0) (- x 12.0)))
     (* (- x 15.0) (- x 14.0)))
    (* (- x 17.0) (- x 16.0))))
  380.0))

C

double code(double x) {
	return ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * 380.0;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = ((x - 18.0d0) * (((((x - 11.0d0) * ((x - 10.0d0) * ((x - 9.0d0) * (((x - 8.0d0) * ((((((x - 5.0d0) * (x - 4.0d0)) * (x - 3.0d0)) * (x - 2.0d0)) * (x - 1.0d0)) * (x - 6.0d0))) * (x - 7.0d0))))) * ((x - 13.0d0) * (x - 12.0d0))) * ((x - 15.0d0) * (x - 14.0d0))) * ((x - 17.0d0) * (x - 16.0d0)))) * 380.0d0
end function

Java

public static double code(double x) {
	return ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * 380.0;
}

Python

def code(x):
	return ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * 380.0

Julia

function code(x)
	return Float64(Float64(Float64(x - 18.0) * Float64(Float64(Float64(Float64(Float64(x - 11.0) * Float64(Float64(x - 10.0) * Float64(Float64(x - 9.0) * Float64(Float64(Float64(x - 8.0) * Float64(Float64(Float64(Float64(Float64(Float64(x - 5.0) * Float64(x - 4.0)) * Float64(x - 3.0)) * Float64(x - 2.0)) * Float64(x - 1.0)) * Float64(x - 6.0))) * Float64(x - 7.0))))) * Float64(Float64(x - 13.0) * Float64(x - 12.0))) * Float64(Float64(x - 15.0) * Float64(x - 14.0))) * Float64(Float64(x - 17.0) * Float64(x - 16.0)))) * 380.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x - 18.0) * (((((x - 11.0) * ((x - 10.0) * ((x - 9.0) * (((x - 8.0) * ((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 6.0))) * (x - 7.0))))) * ((x - 13.0) * (x - 12.0))) * ((x - 15.0) * (x - 14.0))) * ((x - 17.0) * (x - 16.0)))) * 380.0;
end

Wolfram

code[x_] := N[(N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 11.0), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 380.0), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. associate-*l* N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

7. Applied rewrites 97.8%

   \[\leadsto \color{blue}{\left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)} \]

8. Taylor expanded in x around 0

   \[\leadsto \left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \color{blue}{380} \]
9. Step-by-step derivation

10. Applied rewrites 18.9%

    \[\leadsto \left(\left(x - 18\right) \cdot \left(\left(\left(\left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(x - 7\right)\right)\right)\right)\right) \cdot \left(\left(x - 13\right) \cdot \left(x - 12\right)\right)\right) \cdot \left(\left(x - 15\right) \cdot \left(x - 14\right)\right)\right) \cdot \left(\left(x - 17\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \color{blue}{380} \]
11. Add Preprocessing

Alternative 9: 18.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{5} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{elif}\;x \leq 8:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot -8\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(47 \cdot x - 60\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (pow x 5.0) (- x 6.0)) (- x 7.0)) (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (if (<= x 8.0)
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0))
                   (- x 7.0))
                  -8.0)
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (- (* 47.0 x) 60.0)
                   (* (* (- x 1.0) (- x 2.0)) (* (- x 7.0) (- x 6.0))))
                  (- x 8.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0)))))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((((pow(x, 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else if (x <= 8.0) {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((47.0 * x) - 60.0) * (((x - 1.0) * (x - 2.0)) * ((x - 7.0) * (x - 6.0)))) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((((x ** 5.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else if (x <= 8.0d0) then
        tmp = (((((((((((((((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (-8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((((47.0d0 * x) - 60.0d0) * (((x - 1.0d0) * (x - 2.0d0)) * ((x - 7.0d0) * (x - 6.0d0)))) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((((Math.pow(x, 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else if (x <= 8.0) {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((47.0 * x) - 60.0) * (((x - 1.0) * (x - 2.0)) * ((x - 7.0) * (x - 6.0)))) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((((math.pow(x, 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	elif x <= 8.0:
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((((47.0 * x) - 60.0) * (((x - 1.0) * (x - 2.0)) * ((x - 7.0) * (x - 6.0)))) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 5.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	elseif (x <= 8.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * -8.0) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(47.0 * x) - 60.0) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(Float64(x - 7.0) * Float64(x - 6.0)))) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((((x ^ 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	elseif (x <= 8.0)
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((((47.0 * x) - 60.0) * (((x - 1.0) * (x - 2.0)) * ((x - 7.0) * (x - 6.0)))) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 5.0], $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * -8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(47.0 * x), $MachinePrecision] - 60.0), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{5}} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 14.0%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{5}} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 14.0%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{5}} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x < 8

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \color{blue}{-8}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \color{blue}{-8}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 8 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(47 \cdot x - 60\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(47 \cdot x - \color{blue}{60}\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 11.6%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(47 \cdot x - 60\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Applied rewrites 11.6%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(47 \cdot x - 60\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 18.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{elif}\;x \leq 8:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot -8\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(24 + x \cdot \left(35 \cdot x - 50\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (pow x 8.0) (- 1.0 (* 36.0 (/ 1.0 x)))) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (if (<= x 8.0)
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0))
                   (- x 7.0))
                  -8.0)
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (- x 6.0)
                  (* (* (+ 24.0 (* x (- (* 35.0 x) 50.0))) (- x 5.0)) 56.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0)))))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else if (x <= 8.0) {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((x - 6.0) * (((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((x ** 8.0d0) * (1.0d0 - (36.0d0 * (1.0d0 / x)))) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else if (x <= 8.0d0) then
        tmp = (((((((((((((((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (-8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((x - 6.0d0) * (((24.0d0 + (x * ((35.0d0 * x) - 50.0d0))) * (x - 5.0d0)) * 56.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((Math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else if (x <= 8.0) {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((x - 6.0) * (((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	elif x <= 8.0:
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((x - 6.0) * (((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 8.0) * Float64(1.0 - Float64(36.0 * Float64(1.0 / x)))) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	elseif (x <= 8.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * -8.0) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 6.0) * Float64(Float64(Float64(24.0 + Float64(x * Float64(Float64(35.0 * x) - 50.0))) * Float64(x - 5.0)) * 56.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((x ^ 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	elseif (x <= 8.0)
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * -8.0) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((x - 6.0) * (((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 8.0], $MachinePrecision] * N[(1.0 - N[(36.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * -8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(N[(24.0 + N[(x * N[(N[(35.0 * x), $MachinePrecision] - 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * 56.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \color{blue}{\left(1 - 36 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(\color{blue}{1} - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - \color{blue}{36 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 7.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x < 8

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \color{blue}{-8}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \color{blue}{-8}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 8 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \color{blue}{\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{56}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 12.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{56}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\color{blue}{\left(24 + x \cdot \left(35 \cdot x - 50\right)\right)} \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   11. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(24 + \color{blue}{x \cdot \left(35 \cdot x - 50\right)}\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(24 + x \cdot \color{blue}{\left(35 \cdot x - 50\right)}\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

       3. lower--.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(24 + x \cdot \left(35 \cdot x - \color{blue}{50}\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

       4. lower-*.f64 9.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(24 + x \cdot \left(35 \cdot x - 50\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. Applied rewrites 9.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\color{blue}{\left(24 + x \cdot \left(35 \cdot x - 50\right)\right)} \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 18.3% accurate, 1.1× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot 72\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (- x 10.0)
             (*
              (*
               (*
                (* (* (* (- x 5.0) (- x 4.0)) (- x 3.0)) (- x 2.0))
                (- x 1.0))
               (- x 7.0))
              (- x 6.0)))
            72.0)
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return ((((((((((((x - 10.0) * (((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * 72.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = ((((((((((((x - 10.0d0) * (((((((x - 5.0d0) * (x - 4.0d0)) * (x - 3.0d0)) * (x - 2.0d0)) * (x - 1.0d0)) * (x - 7.0d0)) * (x - 6.0d0))) * 72.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return ((((((((((((x - 10.0) * (((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * 72.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return ((((((((((((x - 10.0) * (((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * 72.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 10.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 5.0) * Float64(x - 4.0)) * Float64(x - 3.0)) * Float64(x - 2.0)) * Float64(x - 1.0)) * Float64(x - 7.0)) * Float64(x - 6.0))) * 72.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = ((((((((((((x - 10.0) * (((((((x - 5.0) * (x - 4.0)) * (x - 3.0)) * (x - 2.0)) * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * 72.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 10.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 72.0), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. associate-*l* N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

7. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

8. Taylor expanded in x around 0

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \color{blue}{72}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
9. Step-by-step derivation

10. Applied rewrites 17.6%

    \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \color{blue}{72}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
11. Add Preprocessing

Alternative 12: 17.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{elif}\;x \leq 7:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot -7\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(840 + x \cdot \left(1849 \cdot x - 2038\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (pow x 8.0) (- 1.0 (* 36.0 (/ 1.0 x)))) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (if (<= x 7.0)
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0))
                   -7.0)
                  (- x 8.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (- x 10.0)
                 (* (+ 840.0 (* x (- (* 1849.0 x) 2038.0))) (- x 6.0)))
                (* (- x 9.0) (- x 8.0)))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0)))))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else if (x <= 7.0) {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * -7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((((((((x - 10.0) * ((840.0 + (x * ((1849.0 * x) - 2038.0))) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((x ** 8.0d0) * (1.0d0 - (36.0d0 * (1.0d0 / x)))) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else if (x <= 7.0d0) then
        tmp = (((((((((((((((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (-7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((((x - 10.0d0) * ((840.0d0 + (x * ((1849.0d0 * x) - 2038.0d0))) * (x - 6.0d0))) * ((x - 9.0d0) * (x - 8.0d0))) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((Math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else if (x <= 7.0) {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * -7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((((((((x - 10.0) * ((840.0 + (x * ((1849.0 * x) - 2038.0))) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	elif x <= 7.0:
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * -7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((((((((((((x - 10.0) * ((840.0 + (x * ((1849.0 * x) - 2038.0))) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 8.0) * Float64(1.0 - Float64(36.0 * Float64(1.0 / x)))) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	elseif (x <= 7.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * -7.0) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 10.0) * Float64(Float64(840.0 + Float64(x * Float64(Float64(1849.0 * x) - 2038.0))) * Float64(x - 6.0))) * Float64(Float64(x - 9.0) * Float64(x - 8.0))) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((x ^ 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	elseif (x <= 7.0)
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * -7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((((x - 10.0) * ((840.0 + (x * ((1849.0 * x) - 2038.0))) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 8.0], $MachinePrecision] * N[(1.0 - N[(36.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * -7.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 10.0), $MachinePrecision] * N[(N[(840.0 + N[(x * N[(N[(1849.0 * x), $MachinePrecision] - 2038.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \color{blue}{\left(1 - 36 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(\color{blue}{1} - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - \color{blue}{36 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 7.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x < 7

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{-7}\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 8.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{-7}\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 7 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\color{blue}{\left(840 + x \cdot \left(1849 \cdot x - 2038\right)\right)} \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   9. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(840 + \color{blue}{x \cdot \left(1849 \cdot x - 2038\right)}\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(840 + x \cdot \color{blue}{\left(1849 \cdot x - 2038\right)}\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(840 + x \cdot \left(1849 \cdot x - \color{blue}{2038}\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 9.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(840 + x \cdot \left(1849 \cdot x - 2038\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. Applied rewrites 9.1%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\color{blue}{\left(840 + x \cdot \left(1849 \cdot x - 2038\right)\right)} \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 17.4% accurate, 1.1× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot 42\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (- x 3.0) (* (- x 4.0) (- x 5.0)))
               (* (* (- x 1.0) (- x 2.0)) 42.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((x - 3.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * (((x - 1.0d0) * (x - 2.0d0)) * 42.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * 42.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((x - 3.0) * ((x - 4.0) * (x - 5.0))) * (((x - 1.0) * (x - 2.0)) * 42.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * 42.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. associate-*r* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. associate-*l* N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

6. Taylor expanded in x around 0

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \color{blue}{42}\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
7. Step-by-step derivation

8. Applied rewrites 17.1%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \color{blue}{42}\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
9. Add Preprocessing

Alternative 14: 17.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{5} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (pow x 5.0) (- x 6.0)) (- x 7.0)) (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0))
                 (- x 7.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((((pow(x, 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((((x ** 5.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((((Math.pow(x, 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((((math.pow(x, 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 5.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((((x ^ 5.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 5.0], $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{5}} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 14.0%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{5}} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 14.0%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{5}} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \color{blue}{-20} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \color{blue}{-20} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 17.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (pow x 8.0) (- 1.0 (* 36.0 (/ 1.0 x)))) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0))
                 (- x 7.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((x ** 8.0d0) * (1.0d0 - (36.0d0 * (1.0d0 / x)))) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((Math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 8.0) * Float64(1.0 - Float64(36.0 * Float64(1.0 / x)))) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((x ^ 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 8.0], $MachinePrecision] * N[(1.0 - N[(36.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \color{blue}{\left(1 - 36 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(\color{blue}{1} - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - \color{blue}{36 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 7.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \color{blue}{-20} \]
   6. Step-by-step derivation

   7. Applied rewrites 13.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \color{blue}{-20} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 16.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot -18\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (pow x 8.0) (- 1.0 (* 36.0 (/ 1.0 x)))) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0))
                 (- x 7.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      -18.0)
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * -18.0) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((x ** 8.0d0) * (1.0d0 - (36.0d0 * (1.0d0 / x)))) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (-18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((Math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * -18.0) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * -18.0) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 8.0) * Float64(1.0 - Float64(36.0 * Float64(1.0 / x)))) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * -18.0) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((x ^ 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * -18.0) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 8.0], $MachinePrecision] * N[(1.0 - N[(36.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \color{blue}{\left(1 - 36 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(\color{blue}{1} - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - \color{blue}{36 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 7.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \color{blue}{-18}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 13.0%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \color{blue}{-18}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 16.5% accurate, 1.1× speedup

Math

\[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(20 \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* 20.0 (* (- x 3.0) (* (- x 2.0) (- x 1.0)))) (- x 6.0))
               (- x 7.0))
              (- x 8.0))
             (- x 9.0))
            (- x 10.0))
           (- x 11.0))
          (- x 12.0))
         (- x 13.0))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

C

double code(double x) {
	return (((((((((((((((20.0 * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = (((((((((((((((20.0d0 * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((((((((((((((20.0 * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return (((((((((((((((20.0 * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(20.0 * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((((((((((((((20.0 * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(20.0 * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. associate-*l* N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. lower-*.f64 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. *-commutative N/A

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   12. *-commutative N/A

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   13. lower-*.f64 97.8%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

3. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

4. Taylor expanded in x around 0

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{20} \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
5. Step-by-step derivation

6. Applied rewrites 16.5%

   \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{20} \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
7. Add Preprocessing

Alternative 18: 16.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot -19\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (pow x 8.0) (- 1.0 (* 36.0 (/ 1.0 x)))) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (- x 6.0)
                (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) 56.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     -19.0)
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = (((((((((((((x ** 8.0d0) * (1.0d0 - (36.0d0 * (1.0d0 / x)))) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((x - 6.0d0) * ((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * 56.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (-19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = ((((((((((((Math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = ((((((((((((math.pow(x, 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 8.0) * Float64(1.0 - Float64(36.0 * Float64(1.0 / x)))) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 6.0) * Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * 56.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * -19.0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = (((((((((((((x ^ 8.0) * (1.0 - (36.0 * (1.0 / x)))) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 8.0], $MachinePrecision] * N[(1.0 - N[(36.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * 56.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * -19.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \color{blue}{\left(1 - 36 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(\color{blue}{1} - 36 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - \color{blue}{36 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 7.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 36 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \color{blue}{\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{56}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 12.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{56}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \color{blue}{-19}\right) \cdot \left(x - 20\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 12.3%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \color{blue}{-19}\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 16.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 38 \cdot \frac{1}{x}\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot -19\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 2.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (pow x 8.0) (- 1.0 (* 38.0 (/ 1.0 x))))
              (* (- x 9.0) (- x 8.0)))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (- x 6.0)
                (* (* (* (* 2.0 (- x 3.0)) (- x 4.0)) (- x 5.0)) 56.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     -19.0)
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = (((((((((((pow(x, 8.0) * (1.0 - (38.0 * (1.0 / x)))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (x <= 2.0d0) then
        tmp = ((((((((((((x ** 8.0d0) * (1.0d0 - (38.0d0 * (1.0d0 / x)))) * ((x - 9.0d0) * (x - 8.0d0))) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((x - 6.0d0) * ((((2.0d0 * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * 56.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (-19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = (((((((((((Math.pow(x, 8.0) * (1.0 - (38.0 * (1.0 / x)))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = (((((((((((math.pow(x, 8.0) * (1.0 - (38.0 * (1.0 / x)))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 8.0) * Float64(1.0 - Float64(38.0 * Float64(1.0 / x)))) * Float64(Float64(x - 9.0) * Float64(x - 8.0))) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 6.0) * Float64(Float64(Float64(Float64(2.0 * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * 56.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * -19.0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = ((((((((((((x ^ 8.0) * (1.0 - (38.0 * (1.0 / x)))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((x - 6.0) * ((((2.0 * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * 56.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * -19.0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 8.0], $MachinePrecision] * N[(1.0 - N[(38.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(N[(N[(2.0 * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * 56.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * -19.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 38 \cdot \frac{1}{x}\right)\right)} \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \color{blue}{\left(1 - 38 \cdot \frac{1}{x}\right)}\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(\color{blue}{1} - 38 \cdot \frac{1}{x}\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - \color{blue}{38 \cdot \frac{1}{x}}\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 38 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 8.6%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{8} \cdot \left(1 - 38 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. Applied rewrites 8.6%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{8} \cdot \left(1 - 38 \cdot \frac{1}{x}\right)\right)} \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 2 < x

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{2} \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \color{blue}{\left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)}\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{56}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 12.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{56}\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   10. Taylor expanded in x around 0

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \color{blue}{-19}\right) \cdot \left(x - 20\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 12.3%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(2 \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot 56\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \color{blue}{-19}\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 15.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 4000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(\left(120 \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      4000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (- x 10.0) (* (* (* 120.0 (- x 1.0)) (- x 7.0)) (- x 6.0)))
              (* (- x 9.0) (- x 8.0)))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (* (pow x 14.0) (+ 1.0 (* -1.0 (/ (- 105.0 (* 5005.0 (/ 1.0 x))) x))))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0) {
		tmp = ((((((((((((x - 10.0) * (((120.0 * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 4000000000000.0d0) then
        tmp = ((((((((((((x - 10.0d0) * (((120.0d0 * (x - 1.0d0)) * (x - 7.0d0)) * (x - 6.0d0))) * ((x - 9.0d0) * (x - 8.0d0))) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((x ** 14.0d0) * (1.0d0 + ((-1.0d0) * ((105.0d0 - (5005.0d0 * (1.0d0 / x))) / x)))) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0) {
		tmp = ((((((((((((x - 10.0) * (((120.0 * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((Math.pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0:
		tmp = ((((((((((((x - 10.0) * (((120.0 * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((((((math.pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 4000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 10.0) * Float64(Float64(Float64(120.0 * Float64(x - 1.0)) * Float64(x - 7.0)) * Float64(x - 6.0))) * Float64(Float64(x - 9.0) * Float64(x - 8.0))) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 14.0) * Float64(1.0 + Float64(-1.0 * Float64(Float64(105.0 - Float64(5005.0 * Float64(1.0 / x))) / x)))) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0)
		tmp = ((((((((((((x - 10.0) * (((120.0 * (x - 1.0)) * (x - 7.0)) * (x - 6.0))) * ((x - 9.0) * (x - 8.0))) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((x ^ 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 4000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 10.0), $MachinePrecision] * N[(N[(N[(120.0 * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[Power[x, 14.0], $MachinePrecision] * N[(1.0 + N[(-1.0 * N[(N[(105.0 - N[(5005.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 4e12

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\color{blue}{120} \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 13.1%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 10\right) \cdot \left(\left(\left(\color{blue}{120} \cdot \left(x - 1\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right)\right) \cdot \left(\left(x - 9\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 4e12 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right)} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \color{blue}{\left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(\color{blue}{1} + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + \color{blue}{-1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \color{blue}{\frac{105 - 5005 \cdot \frac{1}{x}}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{\color{blue}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-/.f64 6.8%

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 6.8%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right)} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 15.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 4000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(274 \cdot x - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      4000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (- (* 274.0 x) 120.0) (- x 6.0)) (- x 7.0)) (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (* (pow x 14.0) (+ 1.0 (* -1.0 (/ (- 105.0 (* 5005.0 (/ 1.0 x))) x))))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0) {
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 4000000000000.0d0) then
        tmp = ((((((((((((((((274.0d0 * x) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((x ** 14.0d0) * (1.0d0 + ((-1.0d0) * ((105.0d0 - (5005.0d0 * (1.0d0 / x))) / x)))) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0) {
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((Math.pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0:
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((((((math.pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 4000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(274.0 * x) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 14.0) * Float64(1.0 + Float64(-1.0 * Float64(Float64(105.0 - Float64(5005.0 * Float64(1.0 / x))) / x)))) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 4000000000000.0)
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((x ^ 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 4000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(274.0 * x), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[Power[x, 14.0], $MachinePrecision] * N[(1.0 + N[(-1.0 * N[(N[(105.0 - N[(5005.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 4e12

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(274 \cdot x - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(274 \cdot x - \color{blue}{120}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 12.9%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(274 \cdot x - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 12.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(274 \cdot x - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 4e12 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right)} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \color{blue}{\left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(\color{blue}{1} + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + \color{blue}{-1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \color{blue}{\frac{105 - 5005 \cdot \frac{1}{x}}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{\color{blue}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-/.f64 6.8%

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 6.8%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right)} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 15.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{7} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (pow x 7.0) (- x 8.0)) (- x 9.0)) (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((pow(x, 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 100000000000.0d0) then
        tmp = (((((((((((((x ** 7.0d0) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((Math.pow(x, 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0:
		tmp = ((((((((((((math.pow(x, 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 7.0) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0)
		tmp = (((((((((((((x ^ 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 7.0], $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 1e11

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{7}} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 12.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{7}} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 12.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{7}} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 8.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 14.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (- (* 13068.0 x) 5040.0) (- x 8.0)) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 100000000000.0d0) then
        tmp = ((((((((((((((13068.0d0 * x) - 5040.0d0) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0:
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(13068.0 * x) - 5040.0) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0)
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(13068.0 * x), $MachinePrecision] - 5040.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 1e11

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(13068 \cdot x - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - \color{blue}{5040}\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 11.5%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 11.5%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(13068 \cdot x - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 8.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 14.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (* (pow x 9.0) (- x 10.0)) (- x 11.0)) (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((((pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = (((((((((((x ** 9.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((((Math.pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((((((((math.pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = (((((((((((x ^ 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 9.0], $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{9}} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 10.9%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{9}} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{9}} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 8.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 14.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 1026576.0 x) 362880.0) (- x 10.0)) (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 100000000000.0d0) then
        tmp = ((((((((((((1026576.0d0 * x) - 362880.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0:
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1026576.0 * x) - 362880.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0)
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1026576.0 * x), $MachinePrecision] - 362880.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 1e11

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - \color{blue}{362880}\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 8.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{10}} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 13.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 580000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      580000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 1026576.0 x) 362880.0) (- x 10.0)) (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (* (pow x 14.0) (+ 1.0 (* -1.0 (/ (- 105.0 (* 5005.0 (/ 1.0 x))) x))))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 580000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 580000000000.0d0) then
        tmp = ((((((((((((1026576.0d0 * x) - 362880.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((x ** 14.0d0) * (1.0d0 + ((-1.0d0) * ((105.0d0 - (5005.0d0 * (1.0d0 / x))) / x)))) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 580000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((Math.pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 580000000000.0:
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((((((math.pow(x, 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 580000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1026576.0 * x) - 362880.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 14.0) * Float64(1.0 + Float64(-1.0 * Float64(Float64(105.0 - Float64(5005.0 * Float64(1.0 / x))) / x)))) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 580000000000.0)
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((x ^ 14.0) * (1.0 + (-1.0 * ((105.0 - (5005.0 * (1.0 / x))) / x)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 580000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1026576.0 * x), $MachinePrecision] - 362880.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[Power[x, 14.0], $MachinePrecision] * N[(1.0 + N[(-1.0 * N[(N[(105.0 - N[(5005.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 5.8e11

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - \color{blue}{362880}\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 5.8e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right)} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \color{blue}{\left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(\color{blue}{1} + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + \color{blue}{-1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \color{blue}{\frac{105 - 5005 \cdot \frac{1}{x}}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{\color{blue}{x}}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-/.f64 6.8%

         \[\leadsto \left(\left(\left(\left(\left(\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 6.8%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left({x}^{14} \cdot \left(1 + -1 \cdot \frac{105 - 5005 \cdot \frac{1}{x}}{x}\right)\right)} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 13.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{12} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 1026576.0 x) 362880.0) (- x 10.0)) (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* (pow x 12.0) (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 100000000000.0d0) then
        tmp = ((((((((((((1026576.0d0 * x) - 362880.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((x ** 12.0d0) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((Math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0:
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1026576.0 * x) - 362880.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 12.0) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0)
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((x ^ 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1026576.0 * x), $MachinePrecision] - 362880.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 12.0], $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 1e11

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - \color{blue}{362880}\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{12}} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 7.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{12}} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{12}} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 13.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot -11\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{12} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (*
       (- x 16.0)
       (*
        (*
         (*
          (* (* (* (fma -10628640.0 x 3628800.0) -11.0) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 17.0)))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* (pow x 12.0) (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((x - 16.0) * ((((((fma(-10628640.0, x, 3628800.0) * -11.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 17.0))) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 16.0) * Float64(Float64(Float64(Float64(Float64(Float64(fma(-10628640.0, x, 3628800.0) * -11.0) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 17.0))) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 12.0) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(x - 16.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(-10628640.0 * x + 3628800.0), $MachinePrecision] * -11.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 12.0], $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(3628800 + -10628640 \cdot x\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + \color{blue}{-10628640 \cdot x}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 7.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot \color{blue}{x}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(3628800 + -10628640 \cdot x\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot x\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot x\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right)} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot x\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right)\right)} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Applied rewrites 7.3%

      \[\leadsto \left(\left(\color{blue}{\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot \color{blue}{-11}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 10.3%

       \[\leadsto \left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot \color{blue}{-11}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{12}} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 7.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{\color{blue}{12}} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{{x}^{12}} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot -11\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (*
       (- x 16.0)
       (*
        (*
         (*
          (* (* (* (fma -10628640.0 x 3628800.0) -11.0) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 17.0)))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* 479001600.0 (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((x - 16.0) * ((((((fma(-10628640.0, x, 3628800.0) * -11.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 17.0))) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x - 16.0) * Float64(Float64(Float64(Float64(Float64(Float64(fma(-10628640.0, x, 3628800.0) * -11.0) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 17.0))) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(479001600.0 * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(x - 16.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(-10628640.0 * x + 3628800.0), $MachinePrecision] * -11.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(479001600.0 * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(3628800 + -10628640 \cdot x\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + \color{blue}{-10628640 \cdot x}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 7.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot \color{blue}{x}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(3628800 + -10628640 \cdot x\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot x\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot x\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right)} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. *-commutative N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(3628800 + -10628640 \cdot x\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right)\right)} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Applied rewrites 7.3%

      \[\leadsto \left(\left(\color{blue}{\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot \color{blue}{-11}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 10.3%

       \[\leadsto \left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(\left(\left(\mathsf{fma}\left(-10628640, x, 3628800\right) \cdot \color{blue}{-11}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 17\right)\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 30: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (- (* 120543840.0 x) 39916800.0) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* 479001600.0 (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((((((((120543840.0d0 * x) - 39916800.0d0) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((479001600.0d0 * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(120543840.0 * x) - 39916800.0) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(479001600.0 * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(120543840.0 * x), $MachinePrecision] - 39916800.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(479001600.0 * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - \color{blue}{39916800}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 31: 13.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 19802759040.0 x) 6227020800.0) (- x 14.0)) (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* 479001600.0 (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((((((19802759040.0d0 * x) - 6227020800.0d0) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((479001600.0d0 * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(19802759040.0 * x) - 6227020800.0) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(479001600.0 * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(19802759040.0 * x), $MachinePrecision] - 6227020800.0), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(479001600.0 * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - \color{blue}{6227020800}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 9.6%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.6%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 7.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 32: 13.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 19802759040.0 x) 6227020800.0) (- x 14.0)) (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (* (* (* (* 87178291200.0 (- x 15.0)) (- x 16.0)) (- x 17.0)) (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((((((19802759040.0d0 * x) - 6227020800.0d0) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((87178291200.0d0 * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(19802759040.0 * x) - 6227020800.0) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(87178291200.0 * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(19802759040.0 * x), $MachinePrecision] - 6227020800.0), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(87178291200.0 * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - \color{blue}{6227020800}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 9.6%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.6%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.9%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 33: 13.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left({x}^{15} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (* (* (* (* (pow x 15.0) (- x 16.0)) (- x 17.0)) (- x 18.0)) (- x 19.0))
    (- x 20.0))
   (*
    (*
     (* (* (* (* 87178291200.0 (- x 15.0)) (- x 16.0)) (- x 17.0)) (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((pow(x, 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = (((((x ** 15.0d0) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((87178291200.0d0 * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((Math.pow(x, 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((math.pow(x, 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64((x ^ 15.0) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(87178291200.0 * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = (((((x ^ 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[Power[x, 15.0], $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(87178291200.0 * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\color{blue}{{x}^{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.64 8.9%

         \[\leadsto \left(\left(\left(\left({x}^{\color{blue}{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.9%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{x}^{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.9%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 34: 13.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (* (* (- (* 4339163001600.0 x) 1307674368000.0) (- x 16.0)) (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (* (* (* (* 87178291200.0 (- x 15.0)) (- x 16.0)) (- x 17.0)) (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((((4339163001600.0d0 * x) - 1307674368000.0d0) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((87178291200.0d0 * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(4339163001600.0 * x) - 1307674368000.0) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(87178291200.0 * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((87178291200.0 * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[(N[(4339163001600.0 * x), $MachinePrecision] - 1307674368000.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(87178291200.0 * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(4339163001600 \cdot x - \color{blue}{1307674368000}\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.9%

         \[\leadsto \left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.9%

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.9%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 35: 12.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(20922789888000 \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (*
      (* (* (- (* 4339163001600.0 x) 1307674368000.0) (- x 16.0)) (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (* (* (* 20922789888000.0 (- x 17.0)) (- x 18.0)) (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((((4339163001600.0d0 * x) - 1307674368000.0d0) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((20922789888000.0d0 * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(4339163001600.0 * x) - 1307674368000.0) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(20922789888000.0 * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(N[(N[(4339163001600.0 * x), $MachinePrecision] - 1307674368000.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(20922789888000.0 * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(4339163001600 \cdot x - \color{blue}{1307674368000}\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.9%

         \[\leadsto \left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.9%

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.3%

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 36: 12.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(20922789888000 \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (* (* (* 20922789888000.0 (- x 17.0)) (- x 18.0)) (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((20922789888000.0d0 * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(20922789888000.0 * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(20922789888000.0 * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - \color{blue}{355687428096000}\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.6%

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.6%

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.3%

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 37: 12.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (*
     (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (* (* 6402373705728000.0 (- x 19.0)) (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (6402373705728000.0d0 * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(6402373705728000.0 * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(6402373705728000.0 * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - \color{blue}{355687428096000}\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.6%

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.6%

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.0%

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 38: 12.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(\left(6402373705728000 + -22376988058521600 \cdot x\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (*
    (* (+ 6402373705728000.0 (* -22376988058521600.0 x)) (- x 19.0))
    (- x 20.0))
   (* (* 6402373705728000.0 (- x 19.0)) (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((6402373705728000.0 + (-22376988058521600.0 * x)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((6402373705728000.0d0 + ((-22376988058521600.0d0) * x)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (6402373705728000.0d0 * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((6402373705728000.0 + (-22376988058521600.0 * x)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((6402373705728000.0 + (-22376988058521600.0 * x)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(6402373705728000.0 + Float64(-22376988058521600.0 * x)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(6402373705728000.0 * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((6402373705728000.0 + (-22376988058521600.0 * x)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(6402373705728000.0 + N[(-22376988058521600.0 * x), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(6402373705728000.0 * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\color{blue}{\left(6402373705728000 + -22376988058521600 \cdot x\right)} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(6402373705728000 + \color{blue}{-22376988058521600 \cdot x}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.0%

         \[\leadsto \left(\left(6402373705728000 + -22376988058521600 \cdot \color{blue}{x}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.0%

      \[\leadsto \left(\color{blue}{\left(6402373705728000 + -22376988058521600 \cdot x\right)} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.0%

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 39: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (* (- (* 431565146817638400.0 x) 121645100408832000.0) (- x 20.0))
   (* (* 6402373705728000.0 (- x 19.0)) (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((431565146817638400.0d0 * x) - 121645100408832000.0d0) * (x - 20.0d0)
    else
        tmp = (6402373705728000.0d0 * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0)
	else:
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(431565146817638400.0 * x) - 121645100408832000.0) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(6402373705728000.0 * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	else
		tmp = (6402373705728000.0 * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(431565146817638400.0 * x), $MachinePrecision] - 121645100408832000.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(6402373705728000.0 * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(431565146817638400 \cdot x - \color{blue}{121645100408832000}\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.1%

         \[\leadsto \left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.1%

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.0%

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 40: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (* (- (* 431565146817638400.0 x) 121645100408832000.0) (- x 20.0))
   (* -121645100408832000.0 (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = -121645100408832000.0 * (x - 20.0);
	}
	return tmp;
}

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) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-2000000000.0d0)) then
        tmp = ((431565146817638400.0d0 * x) - 121645100408832000.0d0) * (x - 20.0d0)
    else
        tmp = (-121645100408832000.0d0) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = -121645100408832000.0 * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0:
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0)
	else:
		tmp = -121645100408832000.0 * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = Float64(Float64(Float64(431565146817638400.0 * x) - 121645100408832000.0) * Float64(x - 20.0));
	else
		tmp = Float64(-121645100408832000.0 * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0)
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	else
		tmp = -121645100408832000.0 * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(N[(N[(431565146817638400.0 * x), $MachinePrecision] - 121645100408832000.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(-121645100408832000.0 * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(431565146817638400 \cdot x - \color{blue}{121645100408832000}\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 8.1%

         \[\leadsto \left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.1%

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 5.7%

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 41: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (fma x -8.7529480367616e+18 2.43290200817664e+18)
   (* -121645100408832000.0 (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = fma(x, -8.7529480367616e+18, 2.43290200817664e+18);
	} else {
		tmp = -121645100408832000.0 * (x - 20.0);
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = fma(x, -8.7529480367616e+18, 2.43290200817664e+18);
	else
		tmp = Float64(-121645100408832000.0 * Float64(x - 20.0));
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(x * -8.7529480367616e+18 + 2.43290200817664e+18), $MachinePrecision], N[(-121645100408832000.0 * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.1%

         \[\leadsto 2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot \color{blue}{x} \]

   8. Applied rewrites 8.1%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto -8752948036761600000 \cdot x + \color{blue}{2432902008176640000} \]

      3. lift-*.f64 N/A

         \[\leadsto -8752948036761600000 \cdot x + 2432902008176640000 \]

      4. *-commutative N/A

         \[\leadsto x \cdot -8752948036761600000 + 2432902008176640000 \]

      5. lower-fma.f64 8.1%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   10. Applied rewrites 8.1%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 5.7%

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 42: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -2000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -2000000000.0)
   (fma x -8.7529480367616e+18 2.43290200817664e+18)
   2.43290200817664e+18))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -2000000000.0) {
		tmp = fma(x, -8.7529480367616e+18, 2.43290200817664e+18);
	} else {
		tmp = 2.43290200817664e+18;
	}
	return tmp;
}

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -2000000000.0)
		tmp = fma(x, -8.7529480367616e+18, 2.43290200817664e+18);
	else
		tmp = 2.43290200817664e+18;
	end
	return tmp
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -2000000000.0], N[(x * -8.7529480367616e+18 + 2.43290200817664e+18), $MachinePrecision], 2.43290200817664e+18]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -2e9

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 97.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(x - 5\right) \cdot \left(x - 4\right)\right)} \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      13. lower-*.f64 97.8%

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   3. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 6\right)\right)} \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \color{blue}{\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)} \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 2\right) \cdot \left(x - 1\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \color{blue}{\left(\left(x - 1\right) \cdot \left(x - 2\right)\right)}\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(\left(x - 5\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(x - 7\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Applied rewrites 97.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(\left(\left(x - 3\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 6\right)\right)\right)\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.1%

         \[\leadsto 2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot \color{blue}{x} \]

   8. Applied rewrites 8.1%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto -8752948036761600000 \cdot x + \color{blue}{2432902008176640000} \]

      3. lift-*.f64 N/A

         \[\leadsto -8752948036761600000 \cdot x + 2432902008176640000 \]

      4. *-commutative N/A

         \[\leadsto x \cdot -8752948036761600000 + 2432902008176640000 \]

      5. lower-fma.f64 8.1%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   10. Applied rewrites 8.1%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   if -2e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

      \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000} \]
   3. Step-by-step derivation

   4. Applied rewrites 5.7%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 43: 5.7% accurate, 109.5× speedup

Math

\[2.43290200817664 \cdot 10^{+18} \]

FPCore

(FPCore (x) :precision binary64 2.43290200817664e+18)

C

double code(double x) {
	return 2.43290200817664e+18;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = 2.43290200817664d+18
end function

Java

public static double code(double x) {
	return 2.43290200817664e+18;
}

Python

def code(x):
	return 2.43290200817664e+18

Julia

function code(x)
	return 2.43290200817664e+18
end

MATLAB

function tmp = code(x)
	tmp = 2.43290200817664e+18;
end

Wolfram

code[x_] := 2.43290200817664e+18

Derivation

1. Initial program 97.8%

   \[\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{2432902008176640000} \]
3. Step-by-step derivation

4. Applied rewrites 5.7%

   \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025183 
(FPCore (x)
  :name "(x - 1) to (x - 20)"
  :precision binary64
  :pre (and (<= 1.0 x) (<= x 20.0))
  (* (* (* (* (* (* (* (* (* (* (* (* (* (* (* (* (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0)) (- x 5.0)) (- x 6.0)) (- x 7.0)) (- x 8.0)) (- x 9.0)) (- x 10.0)) (- x 11.0)) (- x 12.0)) (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0)) (- x 17.0)) (- x 18.0)) (- x 19.0)) (- x 20.0)))