(x - 1) to (x - 20)

Percentage Accurate: 97.7% → 97.8%

Time: 15.6s

Alternatives: 36

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: 97.7% 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

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (- x 6.0)
           (*
            (* (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0)) (- x 5.0))
            (*
             (* (- x 8.0) (* (- x 7.0) (- x 10.0)))
             (* (- 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 - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (((x - 8.0) * ((x - 7.0) * (x - 10.0))) * ((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 - 6.0d0) * ((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (((x - 8.0d0) * ((x - 7.0d0) * (x - 10.0d0))) * ((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 - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (((x - 8.0) * ((x - 7.0) * (x - 10.0))) * ((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 - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (((x - 8.0) * ((x - 7.0) * (x - 10.0))) * ((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(x - 6.0) * 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(Float64(Float64(x - 8.0) * Float64(Float64(x - 7.0) * Float64(x - 10.0))) * Float64(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 - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (((x - 8.0) * ((x - 7.0) * (x - 10.0))) * ((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[(x - 6.0), $MachinePrecision] * 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[(N[(N[(x - 8.0), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 97.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*l* N/A

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

3. Applied rewrites 97.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

5. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 97.8%

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

7. Applied rewrites 97.8%

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

Alternative 2: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (- x 13.0)
          (*
           (*
            (*
             (*
              (- x 8.0)
              (*
               (*
                (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                (- x 5.0))
               (- x 6.0)))
             (- x 7.0))
            (- x 9.0))
           (- x 10.0)))
         (* (- x 12.0) (- x 11.0)))
        (- 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 - 13.0) * (((((x - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0))) * ((x - 12.0) * (x - 11.0))) * (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 - 13.0d0) * (((((x - 8.0d0) * ((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0))) * (x - 7.0d0)) * (x - 9.0d0)) * (x - 10.0d0))) * ((x - 12.0d0) * (x - 11.0d0))) * (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 - 13.0) * (((((x - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0))) * ((x - 12.0) * (x - 11.0))) * (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 - 13.0) * (((((x - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0))) * ((x - 12.0) * (x - 11.0))) * (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(x - 13.0) * Float64(Float64(Float64(Float64(Float64(x - 8.0) * 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 - 9.0)) * Float64(x - 10.0))) * Float64(Float64(x - 12.0) * Float64(x - 11.0))) * 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 - 13.0) * (((((x - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0))) * ((x - 12.0) * (x - 11.0))) * (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[(x - 13.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 8.0), $MachinePrecision] * 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]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 12.0), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $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 97.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*l* N/A

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

3. Applied rewrites 97.7%

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

5. Applied rewrites 97.7%

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

Alternative 3: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (- x 8.0)
              (*
               (*
                (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                (- x 5.0))
               (- x 6.0)))
             (- x 7.0))
            (- x 9.0))
           (- x 10.0))
          (- x 11.0))
         (* (- x 13.0) (- x 12.0)))
        (- 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 - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * ((x - 13.0) * (x - 12.0))) * (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 - 8.0d0) * ((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0))) * (x - 7.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * ((x - 13.0d0) * (x - 12.0d0))) * (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 - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * ((x - 13.0) * (x - 12.0))) * (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 - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * ((x - 13.0) * (x - 12.0))) * (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(x - 8.0) * 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 - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(Float64(x - 13.0) * Float64(x - 12.0))) * 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 - 8.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0))) * (x - 7.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * ((x - 13.0) * (x - 12.0))) * (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[(x - 8.0), $MachinePrecision] * 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]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $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 97.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*l* N/A

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

3. Applied rewrites 97.7%

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

5. Applied rewrites 97.8%

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

Alternative 4: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (- x 6.0)
               (*
                (*
                 (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
                 (- x 5.0))
                (- 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 - 6.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (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 - 6.0d0) * ((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (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 - 6.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (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 - 6.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (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(x - 6.0) * Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * 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 - 6.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (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[(x - 6.0), $MachinePrecision] * N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $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. Initial program 97.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-*l* N/A

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

   5. lower-*.f64 N/A

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

   6. lower-*.f64 97.7%

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

3. Applied rewrites 97.7%

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

Alternative 5: 25.3% accurate, 1.0× speedup

Math

\[\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(x \cdot \left(1082 + -57 \cdot x\right) - 6840\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (- x 17.0)
   (*
    (- x 16.0)
    (*
     (- x 15.0)
     (*
      (- x 14.0)
      (*
       (- x 13.0)
       (*
        (- x 12.0)
        (*
         (- x 11.0)
         (*
          (- x 10.0)
          (*
           (- x 9.0)
           (*
            (- x 8.0)
            (*
             (- x 7.0)
             (*
              (* (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0)))) (- x 5.0))
              (- x 6.0)))))))))))))
  (- (* x (+ 1082.0 (* -57.0 x))) 6840.0)))

C

double code(double x) {
	return ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x * (1082.0 + (-57.0 * x))) - 6840.0);
}

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 - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * ((x - 12.0d0) * ((x - 11.0d0) * ((x - 10.0d0) * ((x - 9.0d0) * ((x - 8.0d0) * ((x - 7.0d0) * ((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (x - 6.0d0))))))))))))) * ((x * (1082.0d0 + ((-57.0d0) * x))) - 6840.0d0)
end function

Java

public static double code(double x) {
	return ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x * (1082.0 + (-57.0 * x))) - 6840.0);
}

Python

def code(x):
	return ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x * (1082.0 + (-57.0 * x))) - 6840.0)

Julia

function code(x)
	return Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * Float64(Float64(x - 12.0) * Float64(Float64(x - 11.0) * Float64(Float64(x - 10.0) * Float64(Float64(x - 9.0) * Float64(Float64(x - 8.0) * Float64(Float64(x - 7.0) * Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * Float64(x - 6.0))))))))))))) * Float64(Float64(x * Float64(1082.0 + Float64(-57.0 * x))) - 6840.0))
end

MATLAB

function tmp = code(x)
	tmp = ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x * (1082.0 + (-57.0 * x))) - 6840.0);
end

Wolfram

code[x_] := N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(N[(x - 12.0), $MachinePrecision] * N[(N[(x - 11.0), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * N[(1082.0 + N[(-57.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6840.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.7%

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

3. Applied rewrites 97.7%

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

4. Taylor expanded in x around 0

   \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(x \cdot \left(1082 + -57 \cdot x\right) - 6840\right)} \]
5. Step-by-step derivation

   1. lower--.f64 N/A

      \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(x \cdot \left(1082 + -57 \cdot x\right) - \color{blue}{6840}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(x \cdot \left(1082 + -57 \cdot x\right) - 6840\right) \]

   3. lower-+.f64 N/A

      \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(x \cdot \left(1082 + -57 \cdot x\right) - 6840\right) \]

   4. lower-*.f64 25.3%

      \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(x \cdot \left(1082 + -57 \cdot x\right) - 6840\right) \]

6. Applied rewrites 25.3%

   \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(x \cdot \left(1082 + -57 \cdot x\right) - 6840\right)} \]
7. Add Preprocessing

Alternative 6: 21.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6:\\ \;\;\;\;\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(1082 \cdot x - 6840\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(26 \cdot x - 24\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.0)
   (*
    (*
     (- x 17.0)
     (*
      (- x 16.0)
      (*
       (- x 15.0)
       (*
        (- x 14.0)
        (*
         (- x 13.0)
         (*
          (- x 12.0)
          (*
           (- x 11.0)
           (*
            (- x 10.0)
            (*
             (- x 9.0)
             (*
              (- x 8.0)
              (*
               (- x 7.0)
               (*
                (*
                 (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
                 (- x 5.0))
                (- x 6.0)))))))))))))
    (- (* 1082.0 x) 6840.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- x 1.0) (- (* 26.0 x) 24.0)) (- 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) {
	double tmp;
	if (x <= 6.0) {
		tmp = ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0);
	} else {
		tmp = (((((((((((((((((x - 1.0) * ((26.0 * x) - 24.0)) * (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);
	}
	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 <= 6.0d0) then
        tmp = ((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * ((x - 12.0d0) * ((x - 11.0d0) * ((x - 10.0d0) * ((x - 9.0d0) * ((x - 8.0d0) * ((x - 7.0d0) * ((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (x - 6.0d0))))))))))))) * ((1082.0d0 * x) - 6840.0d0)
    else
        tmp = (((((((((((((((((x - 1.0d0) * ((26.0d0 * x) - 24.0d0)) * (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 if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.0) {
		tmp = ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0);
	} else {
		tmp = (((((((((((((((((x - 1.0) * ((26.0 * x) - 24.0)) * (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);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.0:
		tmp = ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0)
	else:
		tmp = (((((((((((((((((x - 1.0) * ((26.0 * x) - 24.0)) * (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)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.0)
		tmp = Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * Float64(Float64(x - 12.0) * Float64(Float64(x - 11.0) * Float64(Float64(x - 10.0) * Float64(Float64(x - 9.0) * Float64(Float64(x - 8.0) * Float64(Float64(x - 7.0) * Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * Float64(x - 6.0))))))))))))) * Float64(Float64(1082.0 * x) - 6840.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(Float64(26.0 * x) - 24.0)) * 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
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.0)
		tmp = ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0);
	else
		tmp = (((((((((((((((((x - 1.0) * ((26.0 * x) - 24.0)) * (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
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.0], N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(N[(x - 12.0), $MachinePrecision] * N[(N[(x - 11.0), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1082.0 * x), $MachinePrecision] - 6840.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(N[(26.0 * x), $MachinePrecision] - 24.0), $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]]

Derivation

1. Split input into 2 regimes

2. if x < 6

   1. Initial program 97.7%

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(1082 \cdot x - 6840\right)} \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(1082 \cdot x - \color{blue}{6840}\right) \]

      2. lower-*.f64 15.0%

         \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(1082 \cdot x - 6840\right) \]

   6. Applied rewrites 15.0%

      \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(1082 \cdot x - 6840\right)} \]

   if 6 < x

   1. Initial program 97.7%

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

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \color{blue}{\left(26 \cdot x - 24\right)}\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(26 \cdot x - \color{blue}{24}\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 11.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(26 \cdot x - 24\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 11.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \color{blue}{\left(26 \cdot x - 24\right)}\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 20.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   -20.0
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (- x 12.0)
          (*
           (*
            (*
             (*
              (* (* (- 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 11.0) (- x 10.0)))
        (- x 13.0))
       (- x 14.0))
      (- x 15.0))
     (- x 16.0))
    (- x 17.0)))
  (* (- x 19.0) (- x 18.0))))

C

double code(double x) {
	return (-20.0 * ((((((((x - 12.0) * (((((((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 - 11.0) * (x - 10.0))) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0))) * ((x - 19.0) * (x - 18.0));
}

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 - 12.0d0) * (((((((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 - 11.0d0) * (x - 10.0d0))) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0))) * ((x - 19.0d0) * (x - 18.0d0))
end function

Java

public static double code(double x) {
	return (-20.0 * ((((((((x - 12.0) * (((((((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 - 11.0) * (x - 10.0))) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0))) * ((x - 19.0) * (x - 18.0));
}

Python

def code(x):
	return (-20.0 * ((((((((x - 12.0) * (((((((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 - 11.0) * (x - 10.0))) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0))) * ((x - 19.0) * (x - 18.0))

Julia

function code(x)
	return Float64(Float64(-20.0 * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 12.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 5.0) * Float64(Float64(x - 4.0) * 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(Float64(x - 11.0) * Float64(x - 10.0))) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0))) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))
end

MATLAB

function tmp = code(x)
	tmp = (-20.0 * ((((((((x - 12.0) * (((((((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 - 11.0) * (x - 10.0))) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0))) * ((x - 19.0) * (x - 18.0));
end

Wolfram

code[x_] := N[(N[(-20.0 * N[(N[(N[(N[(N[(N[(N[(N[(x - 12.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(x - 5.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $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]), $MachinePrecision] * N[(N[(x - 11.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $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]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*l* N/A

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

3. Applied rewrites 97.7%

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

4. Taylor expanded in x around 0

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

6. Applied rewrites 20.8%

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

8. Applied rewrites 20.8%

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

Alternative 8: 18.0% accurate, 1.1× speedup

Math

\[\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot -6840 \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (- x 17.0)
   (*
    (- x 16.0)
    (*
     (- x 15.0)
     (*
      (- x 14.0)
      (*
       (- x 13.0)
       (*
        (- x 12.0)
        (*
         (- x 11.0)
         (*
          (- x 10.0)
          (*
           (- x 9.0)
           (*
            (- x 8.0)
            (*
             (- x 7.0)
             (*
              (* (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0)))) (- x 5.0))
              (- x 6.0)))))))))))))
  -6840.0))

C

double code(double x) {
	return ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * -6840.0;
}

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 - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * ((x - 12.0d0) * ((x - 11.0d0) * ((x - 10.0d0) * ((x - 9.0d0) * ((x - 8.0d0) * ((x - 7.0d0) * ((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (x - 6.0d0))))))))))))) * (-6840.0d0)
end function

Java

public static double code(double x) {
	return ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * -6840.0;
}

Python

def code(x):
	return ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * -6840.0

Julia

function code(x)
	return Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * Float64(Float64(x - 12.0) * Float64(Float64(x - 11.0) * Float64(Float64(x - 10.0) * Float64(Float64(x - 9.0) * Float64(Float64(x - 8.0) * Float64(Float64(x - 7.0) * Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * Float64(x - 6.0))))))))))))) * -6840.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * ((x - 12.0) * ((x - 11.0) * ((x - 10.0) * ((x - 9.0) * ((x - 8.0) * ((x - 7.0) * ((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * -6840.0;
end

Wolfram

code[x_] := N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(N[(x - 12.0), $MachinePrecision] * N[(N[(x - 11.0), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(x - 9.0), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -6840.0), $MachinePrecision]

Derivation

1. Initial program 97.7%

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

3. Applied rewrites 97.7%

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

4. Taylor expanded in x around 0

   \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{-6840} \]
5. Step-by-step derivation

6. Applied rewrites 18.0%

   \[\leadsto \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{-6840} \]
7. Add Preprocessing

Alternative 9: 17.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6.7:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(-560 \cdot \left(\left(x - 9\right) \cdot \left(x - 11\right)\right)\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.7)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (- x 6.0)
             (*
              (* (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0)) (- x 5.0))
              (* -560.0 (* (- 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))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (+ 720.0 (* x (- (* 1624.0 x) 1764.0)))
              (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 6.7) {
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (-560.0 * ((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);
	} else {
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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 <= 6.7d0) then
        tmp = ((((((((((x - 6.0d0) * ((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * ((-560.0d0) * ((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)
    else
        tmp = (((((((((((720.0d0 + (x * ((1624.0d0 * x) - 1764.0d0))) * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.7) {
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (-560.0 * ((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);
	} else {
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.7:
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (-560.0 * ((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)
	else:
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.7)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 6.0) * 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(-560.0 * Float64(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));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(720.0 + Float64(x * Float64(Float64(1624.0 * x) - 1764.0))) * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.7)
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (-560.0 * ((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);
	else
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.7], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 6.0), $MachinePrecision] * 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[(-560.0 * N[(N[(x - 9.0), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(720.0 + N[(x * N[(N[(1624.0 * x), $MachinePrecision] - 1764.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.7000000000000002

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\color{blue}{-560} \cdot \left(\left(x - 9\right) \cdot \left(x - 11\right)\right)\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 12.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(\color{blue}{-560} \cdot \left(\left(x - 9\right) \cdot \left(x - 11\right)\right)\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 6.7000000000000002 < x

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + \color{blue}{x \cdot \left(1624 \cdot x - 1764\right)}\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \color{blue}{\left(1624 \cdot x - 1764\right)}\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - \color{blue}{1764}\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      4. lower-*.f64 10.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

   9. Applied rewrites 10.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 17.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6.4:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot 5040\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.4)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
                (- x 5.0))
               (- x 6.0))
              5040.0)
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (+ 720.0 (* x (- (* 1624.0 x) 1764.0)))
              (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 6.4) {
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (x - 12.0)) * (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 = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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 <= 6.4d0) then
        tmp = ((((((((((((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (x - 6.0d0)) * 5040.0d0) * (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 = (((((((((((720.0d0 + (x * ((1624.0d0 * x) - 1764.0d0))) * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.4) {
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (x - 12.0)) * (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 = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.4:
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (x - 12.0)) * (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 = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.4)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * Float64(x - 6.0)) * 5040.0) * 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(720.0 + Float64(x * Float64(Float64(1624.0 * x) - 1764.0))) * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.4)
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (x - 12.0)) * (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 = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.4], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * 5040.0), $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], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(720.0 + N[(x * N[(N[(1624.0 * x), $MachinePrecision] - 1764.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.4000000000000004

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{5040}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 15.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{5040}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 6.4000000000000004 < x

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + \color{blue}{x \cdot \left(1624 \cdot x - 1764\right)}\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \color{blue}{\left(1624 \cdot x - 1764\right)}\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - \color{blue}{1764}\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      4. lower-*.f64 10.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

   9. Applied rewrites 10.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 17.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6.4:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot 5040\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.4)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
                (- x 5.0))
               (- x 6.0))
              5040.0)
             (- x 11.0))
            (- 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)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (+ 720.0 (* x (- (* 1624.0 x) 1764.0)))
              (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 6.4) {
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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;
	} else {
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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 <= 6.4d0) then
        tmp = ((((((((((((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (x - 6.0d0)) * 5040.0d0) * (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)
    else
        tmp = (((((((((((720.0d0 + (x * ((1624.0d0 * x) - 1764.0d0))) * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.4) {
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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;
	} else {
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.4:
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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
	else:
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.4)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * Float64(x - 6.0)) * 5040.0) * 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);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(720.0 + Float64(x * Float64(Float64(1624.0 * x) - 1764.0))) * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.4)
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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;
	else
		tmp = (((((((((((720.0 + (x * ((1624.0 * x) - 1764.0))) * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.4], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * 5040.0), $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] * -20.0), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(720.0 + N[(x * N[(N[(1624.0 * x), $MachinePrecision] - 1764.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.4000000000000004

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{5040}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 14.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{5040}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

   if 6.4000000000000004 < x

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + \color{blue}{x \cdot \left(1624 \cdot x - 1764\right)}\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \color{blue}{\left(1624 \cdot x - 1764\right)}\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - \color{blue}{1764}\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

      4. lower-*.f64 10.1%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right) \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

   9. Applied rewrites 10.1%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 16.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6.2:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot 5040\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.2)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (* (- x 4.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
                (- x 5.0))
               (- x 6.0))
              5040.0)
             (- x 11.0))
            (- 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)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* 720.0 (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 6.2) {
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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;
	} else {
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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 <= 6.2d0) then
        tmp = ((((((((((((((x - 4.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * (x - 5.0d0)) * (x - 6.0d0)) * 5040.0d0) * (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)
    else
        tmp = ((((((((((720.0d0 * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.2) {
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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;
	} else {
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.2:
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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
	else:
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.2)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 4.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(x - 5.0)) * Float64(x - 6.0)) * 5040.0) * 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);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(720.0 * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.2)
		tmp = ((((((((((((((x - 4.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * (x - 5.0)) * (x - 6.0)) * 5040.0) * (x - 11.0)) * (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;
	else
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.2], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * 5040.0), $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] * -20.0), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(720.0 * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.2000000000000002

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{5040}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 14.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \color{blue}{5040}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]

   if 6.2000000000000002 < x

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 9.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 16.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot -55440\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (- x 6.0)
             (*
              (* (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0)) (- x 5.0))
              -55440.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* 720.0 (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -20.0)))

C

double code(double x) {
	double tmp;
	if (x <= 6.0) {
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * -55440.0)) * (x - 12.0)) * (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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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 <= 6.0d0) then
        tmp = ((((((((((x - 6.0d0) * ((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (-55440.0d0))) * (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 = ((((((((((720.0d0 * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.0) {
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * -55440.0)) * (x - 12.0)) * (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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.0:
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * -55440.0)) * (x - 12.0)) * (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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 6.0) * 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)) * -55440.0)) * 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(720.0 * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.0)
		tmp = ((((((((((x - 6.0) * ((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * -55440.0)) * (x - 12.0)) * (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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 6.0), $MachinePrecision] * 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] * -55440.0), $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[(720.0 * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{-55440}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 11.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 6\right) \cdot \left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \color{blue}{-55440}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 6 < x

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 9.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 14.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -1100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

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))
      -1100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (* (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))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* 720.0 (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -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)) <= -1100000000000.0) {
		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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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)) <= (-1100000000000.0d0)) 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 = ((((((((((720.0d0 * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-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)) <= -1100000000000.0) {
		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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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)) <= -1100000000000.0:
		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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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)) <= -1100000000000.0)
		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(Float64(720.0 * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -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)) <= -1100000000000.0)
		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 = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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], -1100000000000.0], 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[(720.0 * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $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))) < -1.1e12

   1. Initial program 97.7%

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

   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.f64 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 -1.1e12 < (*.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 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 9.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 14.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -1100000000000:\\ \;\;\;\;\left(\left(\left(\left({x}^{15} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

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))
      -1100000000000.0)
   (*
    (* (* (* (* (pow x 15.0) (- x 16.0)) (- x 17.0)) (- x 18.0)) (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* 720.0 (* (* (- x 8.0) (- x 7.0)) (* (- x 10.0) (- 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))
    -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)) <= -1100000000000.0) {
		tmp = ((((pow(x, 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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)) <= (-1100000000000.0d0)) then
        tmp = (((((x ** 15.0d0) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((720.0d0 * (((x - 8.0d0) * (x - 7.0d0)) * ((x - 10.0d0) * (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)) * (-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)) <= -1100000000000.0) {
		tmp = ((((Math.pow(x, 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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)) <= -1100000000000.0:
		tmp = ((((math.pow(x, 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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)) <= -1100000000000.0)
		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(Float64(Float64(Float64(Float64(Float64(720.0 * Float64(Float64(Float64(x - 8.0) * Float64(x - 7.0)) * Float64(Float64(x - 10.0) * 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)) * -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)) <= -1100000000000.0)
		tmp = (((((x ^ 15.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((720.0 * (((x - 8.0) * (x - 7.0)) * ((x - 10.0) * (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)) * -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], -1100000000000.0], 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[(N[(N[(N[(N[(N[(720.0 * N[(N[(N[(x - 8.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $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] * -20.0), $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))) < -1.1e12

   1. Initial program 97.7%

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

   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.f64 9.0%

         \[\leadsto \left(\left(\left(\left({x}^{\color{blue}{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.0%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{x}^{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -1.1e12 < (*.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 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 9.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{720} \cdot \left(\left(\left(x - 8\right) \cdot \left(x - 7\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 14.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 30000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      30000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 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)) <= 30000000000.0) {
		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)) <= 30000000000.0d0) 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)) <= 30000000000.0) {
		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)) <= 30000000000.0:
		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)) <= 30000000000.0)
		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)) <= 30000000000.0)
		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], 30000000000.0], 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))) < 3e10

   1. Initial program 97.7%

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

   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 10.9%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 3e10 < (*.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 97.7%

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

   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.f64 8.0%

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

   4. Applied rewrites 8.0%

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

Alternative 17: 13.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 560000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right) \cdot -14\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      560000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 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 13.0) (- 1.0 (* 91.0 (/ 1.0 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)) <= 560000000000.0) {
		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, 13.0) * (1.0 - (91.0 * (1.0 / 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)) <= 560000000000.0d0) 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 ** 13.0d0) * (1.0d0 - (91.0d0 * (1.0d0 / 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)) <= 560000000000.0) {
		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, 13.0) * (1.0 - (91.0 * (1.0 / 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)) <= 560000000000.0:
		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, 13.0) * (1.0 - (91.0 * (1.0 / 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)) <= 560000000000.0)
		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 ^ 13.0) * Float64(1.0 - Float64(91.0 * Float64(1.0 / 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)) <= 560000000000.0)
		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 ^ 13.0) * (1.0 - (91.0 * (1.0 / 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], 560000000000.0], 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, 13.0], $MachinePrecision] * N[(1.0 - N[(91.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -14.0), $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))) < 5.6e11

   1. Initial program 97.7%

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

   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 10.9%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.9%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(1026576 \cdot x - 362880\right)} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 5.6e11 < (*.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 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \color{blue}{\left(1 - 91 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\color{blue}{1} - 91 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - \color{blue}{91 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 5.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Applied rewrites 5.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right) \cdot \color{blue}{-14}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 6.7%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right) \cdot \color{blue}{-14}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 13.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right) \cdot -14\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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))
   (*
    (*
     (*
      (*
       (*
        (* (* (* (pow x 13.0) (- 1.0 (* 91.0 (/ 1.0 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)) <= -40000000000.0) {
		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 = (((((((pow(x, 13.0) * (1.0 - (91.0 * (1.0 / 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)) <= (-40000000000.0d0)) 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 = ((((((((x ** 13.0d0) * (1.0d0 - (91.0d0 * (1.0d0 / 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)) <= -40000000000.0) {
		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 = (((((((Math.pow(x, 13.0) * (1.0 - (91.0 * (1.0 / 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)) <= -40000000000.0:
		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 = (((((((math.pow(x, 13.0) * (1.0 - (91.0 * (1.0 / 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)) <= -40000000000.0)
		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((x ^ 13.0) * Float64(1.0 - Float64(91.0 * Float64(1.0 / 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)) <= -40000000000.0)
		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 = ((((((((x ^ 13.0) * (1.0 - (91.0 * (1.0 / 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], -40000000000.0], 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[(N[Power[x, 13.0], $MachinePrecision] * N[(1.0 - N[(91.0 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * -14.0), $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))) < -4e10

   1. Initial program 97.7%

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

   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 9.7%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \color{blue}{\left(1 - 91 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\color{blue}{1} - 91 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - \color{blue}{91 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 5.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   8. Applied rewrites 5.4%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right) \cdot \color{blue}{-14}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 6.7%

       \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(1 - 91 \cdot \frac{1}{x}\right)\right) \cdot \color{blue}{-14}\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 13.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{12} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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))
   (*
    (*
     (*
      (*
       (* (* (* (* (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)) <= -40000000000.0) {
		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 = (((((((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)) <= (-40000000000.0d0)) 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 = ((((((((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)) <= -40000000000.0) {
		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 = (((((((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)) <= -40000000000.0:
		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 = (((((((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)) <= -40000000000.0)
		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((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)) <= -40000000000.0)
		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 = ((((((((x ^ 12.0) * (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], -40000000000.0], 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[(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))) < -4e10

   1. Initial program 97.7%

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

   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 9.7%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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.f64 7.2%

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

   4. Applied rewrites 7.2%

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

Alternative 20: 13.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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))
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* (* 3628800.0 (- x 11.0)) (- x 12.0)) (- 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)) <= -40000000000.0) {
		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 = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (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)) <= (-40000000000.0d0)) 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 = (((((((((3628800.0d0 * (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)) <= -40000000000.0) {
		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 = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (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)) <= -40000000000.0:
		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 = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (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)) <= -40000000000.0)
		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(Float64(Float64(3628800.0 * 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)) <= -40000000000.0)
		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 = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (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], -40000000000.0], 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[(N[(N[(3628800.0 * 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))) < -4e10

   1. Initial program 97.7%

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

   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 9.7%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{3628800} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 7.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{3628800} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 13.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 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))
      -40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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))
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* (* 3628800.0 (- x 11.0)) (- 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 - 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)) <= -40000000000.0) {
		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 = (((((((((3628800.0 * (x - 11.0)) * (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 - 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)) <= (-40000000000.0d0)) 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 = (((((((((3628800.0d0 * (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 - 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)) <= -40000000000.0) {
		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 = (((((((((3628800.0 * (x - 11.0)) * (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 - 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)) <= -40000000000.0:
		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 = (((((((((3628800.0 * (x - 11.0)) * (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 (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)) <= -40000000000.0)
		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(Float64(Float64(3628800.0 * 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 - 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)) <= -40000000000.0)
		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 = (((((((((3628800.0 * (x - 11.0)) * (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[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], -40000000000.0], 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[(N[(N[(3628800.0 * 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 (*.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))) < -4e10

   1. Initial program 97.7%

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

   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 9.7%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

   7. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{3628800} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
   8. Step-by-step derivation

   9. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{3628800} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 13.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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 9.7%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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 7.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 13.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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 9.7%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.7%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left(19802759040 \cdot x - 6227020800\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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 6.8%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 13.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left({x}^{15} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (* (* (* (* (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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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.f64 9.0%

         \[\leadsto \left(\left(\left(\left({x}^{\color{blue}{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.0%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{x}^{15}} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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 6.8%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 13.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (* (* (- (* 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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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 9.1%

         \[\leadsto \left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.1%

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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 6.8%

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 12.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left({x}^{18} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (*
      (* (* (- (* 4339163001600.0 x) 1307674368000.0) (- x 16.0)) (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (* (* (pow 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)) <= -40000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (pow(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)) <= (-40000000000.0d0)) then
        tmp = ((((((4339163001600.0d0 * x) - 1307674368000.0d0) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((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)) <= -40000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (Math.pow(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)) <= -40000000000.0:
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (math.pow(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)) <= -40000000000.0)
		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((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)) <= -40000000000.0)
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((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], -40000000000.0], 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[Power[x, 18.0], $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))) < -4e10

   1. Initial program 97.7%

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

   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 9.1%

         \[\leadsto \left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.1%

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{{x}^{18}} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.f64 5.8%

         \[\leadsto \left({x}^{\color{blue}{18}} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 5.8%

      \[\leadsto \left(\color{blue}{{x}^{18}} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 12.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left({x}^{18} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (* (* (pow 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)) <= -40000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (pow(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)) <= (-40000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((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)) <= -40000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (Math.pow(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)) <= -40000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (math.pow(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)) <= -40000000000.0)
		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((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)) <= -40000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((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], -40000000000.0], 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[Power[x, 18.0], $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))) < -4e10

   1. Initial program 97.7%

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

   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 8.7%

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.7%

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{{x}^{18}} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-pow.f64 5.8%

         \[\leadsto \left({x}^{\color{blue}{18}} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 5.8%

      \[\leadsto \left(\color{blue}{{x}^{18}} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 12.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(20922789888000 \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (* (- (* 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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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 8.7%

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.7%

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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 6.2%

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 12.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

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))
      -40000000000.0)
   (*
    (*
     (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (pow 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)) <= -40000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = pow(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)) <= (-40000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = 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)) <= -40000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = Math.pow(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)) <= -40000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = math.pow(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)) <= -40000000000.0)
		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 = 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)) <= -40000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = 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], -40000000000.0], 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[Power[x, 20.0], $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))) < -4e10

   1. Initial program 97.7%

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

   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 8.7%

         \[\leadsto \left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.7%

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{20}} \]
   3. Step-by-step derivation

      1. lower-pow.f64 5.7%

         \[\leadsto {x}^{\color{blue}{20}} \]

   4. Applied rewrites 5.7%

      \[\leadsto \color{blue}{{x}^{20}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 30: 12.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

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))
      -40000000000.0)
   (* (- (* 431565146817638400.0 x) 121645100408832000.0) (- x 20.0))
   (pow 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)) <= -40000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = pow(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)) <= (-40000000000.0d0)) then
        tmp = ((431565146817638400.0d0 * x) - 121645100408832000.0d0) * (x - 20.0d0)
    else
        tmp = 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)) <= -40000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = Math.pow(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)) <= -40000000000.0:
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0)
	else:
		tmp = math.pow(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)) <= -40000000000.0)
		tmp = Float64(Float64(Float64(431565146817638400.0 * x) - 121645100408832000.0) * Float64(x - 20.0));
	else
		tmp = 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)) <= -40000000000.0)
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	else
		tmp = 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], -40000000000.0], N[(N[(N[(431565146817638400.0 * x), $MachinePrecision] - 121645100408832000.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[Power[x, 20.0], $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))) < -4e10

   1. Initial program 97.7%

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

   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 8.2%

         \[\leadsto \left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.2%

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{20}} \]
   3. Step-by-step derivation

      1. lower-pow.f64 5.7%

         \[\leadsto {x}^{\color{blue}{20}} \]

   4. Applied rewrites 5.7%

      \[\leadsto \color{blue}{{x}^{20}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 31: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (* (- (* 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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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 8.2%

         \[\leadsto \left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.2%

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   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 5.9%

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 32: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (* (- (* 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)) <= -40000000000.0) {
		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)) <= (-40000000000.0d0)) 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)) <= -40000000000.0) {
		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)) <= -40000000000.0:
		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)) <= -40000000000.0)
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

   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 8.2%

         \[\leadsto \left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 8.2%

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 5.6%

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 33: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -40000000000.0)
   (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)) <= -40000000000.0) {
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   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 8.2%

         \[\leadsto 2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot \color{blue}{x} \]

   8. Applied rewrites 8.2%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   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 8.2%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   10. Applied rewrites 8.2%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 5.6%

      \[\leadsto \color{blue}{-121645100408832000} \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 34: 12.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -40000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

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))
      -40000000000.0)
   (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)) <= -40000000000.0) {
		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)) <= -40000000000.0)
		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], -40000000000.0], 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))) < -4e10

   1. Initial program 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

   3. Applied rewrites 97.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   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 8.2%

         \[\leadsto 2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot \color{blue}{x} \]

   8. Applied rewrites 8.2%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   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 8.2%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   10. Applied rewrites 8.2%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{-8.7529480367616 \cdot 10^{+18}}, 2.43290200817664 \cdot 10^{+18}\right) \]

   if -4e10 < (*.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 97.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000} \]
   3. Step-by-step derivation

   4. Applied rewrites 5.5%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 35: 5.5% 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 97.7%

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

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{2432902008176640000} \]
3. Step-by-step derivation

4. Applied rewrites 5.5%

   \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025189 
(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)))