(x - 1) to (x - 20)

Percentage Accurate: 97.8% → 97.8%

Time: 17.8s

Alternatives: 50

Speedup: 1.0×

Specification

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

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

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 4.0) (- x 5.0))
            (*
             (* (* (- x 3.0) (* (- x 2.0) (- x 1.0))) (- x 6.0))
             (fma (- x 8.0) x (* (- x 8.0) -7.0)))))))))))))
  (* (- x 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * fma((x - 8.0), x, ((x - 8.0) * -7.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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(Float64(x - 4.0) * Float64(x - 5.0)) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0))) * Float64(x - 6.0)) * fma(Float64(x - 8.0), x, Float64(Float64(x - 8.0) * -7.0))))))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * x + N[(N[(x - 8.0), $MachinePrecision] * -7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. associate-*l* N/A

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

   13. *-commutative N/A

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

   14. associate-*l* N/A

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

5. Applied rewrites 97.8%

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

7. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.8%

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

9. Applied rewrites 97.8%

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

Alternative 2: 97.8% accurate, 1.0× speedup

Math

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

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 4.0) (- x 5.0))
            (*
             (* (* (- x 3.0) (* (- x 2.0) (- x 1.0))) (- x 6.0))
             (* (- x 7.0) (- x 8.0)))))))))))))
  (* (- x 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 4.0d0) * (x - 5.0d0)) * ((((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0))) * (x - 6.0d0)) * ((x - 7.0d0) * (x - 8.0d0))))))))))))) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))

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(Float64(x - 4.0) * Float64(x - 5.0)) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0))) * Float64(x - 6.0)) * Float64(Float64(x - 7.0) * Float64(x - 8.0))))))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
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[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. associate-*l* N/A

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

   13. *-commutative N/A

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

   14. associate-*l* N/A

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

5. Applied rewrites 97.8%

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

7. Applied rewrites 97.8%

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

Alternative 3: 97.8% accurate, 1.0× speedup

Math

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

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 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0)) (- x 5.0))
            (- x 7.0))
           (* (- x 6.0) (* (- x 8.0) (- x 9.0))))))))))))
  (* (- x 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 7.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 7.0d0)) * ((x - 6.0d0) * ((x - 8.0d0) * (x - 9.0d0)))))))))))) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 7.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 7.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))

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(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 - 7.0)) * Float64(Float64(x - 6.0) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 7.0)) * ((x - 6.0) * ((x - 8.0) * (x - 9.0)))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
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[(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 - 7.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

5. Applied rewrites 97.8%

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

Alternative 4: 97.8% accurate, 1.0× speedup

Math

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

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 5.0)) (* (* (- x 2.0) (- x 1.0)) (- x 6.0)))
              (- x 3.0)))))))))))))
  (* (- x 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 5.0)) * (((x - 2.0) * (x - 1.0)) * (x - 6.0))) * (x - 3.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 5.0d0)) * (((x - 2.0d0) * (x - 1.0d0)) * (x - 6.0d0))) * (x - 3.0d0))))))))))))) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 5.0)) * (((x - 2.0) * (x - 1.0)) * (x - 6.0))) * (x - 3.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 5.0)) * (((x - 2.0) * (x - 1.0)) * (x - 6.0))) * (x - 3.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))

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(x - 5.0)) * Float64(Float64(Float64(x - 2.0) * Float64(x - 1.0)) * Float64(x - 6.0))) * Float64(x - 3.0))))))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 5.0)) * (((x - 2.0) * (x - 1.0)) * (x - 6.0))) * (x - 3.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
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[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. associate-*l* N/A

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

   13. *-commutative N/A

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

   14. associate-*l* N/A

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

5. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*r* N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

7. Applied rewrites 97.8%

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

Alternative 5: 97.8% accurate, 1.0× speedup

Math

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

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 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 18.0) * ((x - 20.0) * (x - 19.0)))

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 - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 18.0) * ((x - 20.0) * (x - 19.0)));
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 - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 6: 97.8% accurate, 1.0× speedup

Math

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

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 2.0) (* (- x 1.0) (* (- x 3.0) (- x 4.0)))) (- x 5.0))
              (- x 6.0)))))))))))))
  (* (- x 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 2.0) * ((x - 1.0) * ((x - 3.0) * (x - 4.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 2.0d0) * ((x - 1.0d0) * ((x - 3.0d0) * (x - 4.0d0)))) * (x - 5.0d0)) * (x - 6.0d0))))))))))))) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 2.0) * ((x - 1.0) * ((x - 3.0) * (x - 4.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 2.0) * ((x - 1.0) * ((x - 3.0) * (x - 4.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))

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 - 2.0) * Float64(Float64(x - 1.0) * Float64(Float64(x - 3.0) * Float64(x - 4.0)))) * Float64(x - 5.0)) * Float64(x - 6.0))))))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 2.0) * ((x - 1.0) * ((x - 3.0) * (x - 4.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
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 - 2.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(x - 4.0), $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 - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. lower-*.f64 N/A

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

   10. lower-*.f64 97.8%

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

5. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*r* N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-*r* N/A

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

   8. *-commutative N/A

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

   9. *-commutative N/A

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

   10. lift-*.f64 N/A

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

   11. associate-*l* N/A

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

   12. lower-*.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lower-*.f64 97.8%

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

7. Applied rewrites 97.8%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

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 4.0)
           (*
            (*
             (*
              (* (* (- x 6.0) (* (* (- x 1.0) (- x 2.0)) (- x 3.0))) (- x 8.0))
              (- x 7.0))
             (- x 5.0))
            (- x 9.0)))))))))))
  (* (- x 18.0) (* (- x 20.0) (- x 19.0)))))

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 - 4.0) * ((((((x - 6.0) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * (x - 8.0)) * (x - 7.0)) * (x - 5.0)) * (x - 9.0))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 4.0d0) * ((((((x - 6.0d0) * (((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0))) * (x - 8.0d0)) * (x - 7.0d0)) * (x - 5.0d0)) * (x - 9.0d0))))))))))) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 4.0) * ((((((x - 6.0) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * (x - 8.0)) * (x - 7.0)) * (x - 5.0)) * (x - 9.0))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 4.0) * ((((((x - 6.0) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * (x - 8.0)) * (x - 7.0)) * (x - 5.0)) * (x - 9.0))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))

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 - 4.0) * Float64(Float64(Float64(Float64(Float64(Float64(x - 6.0) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0))) * Float64(x - 8.0)) * Float64(x - 7.0)) * Float64(x - 5.0)) * Float64(x - 9.0))))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 4.0) * ((((((x - 6.0) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * (x - 8.0)) * (x - 7.0)) * (x - 5.0)) * (x - 9.0))))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
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 - 4.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. associate-*l* N/A

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

   13. *-commutative N/A

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

   14. associate-*l* N/A

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

5. Applied rewrites 97.8%

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

7. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

   8. lower-*.f64 N/A

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

9. Applied rewrites 97.8%

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

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

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 - 10.0) * ((((((((((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 - 11.0))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

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 - 10.0d0) * ((((((((((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 - 11.0d0))))))))) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
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 - 10.0) * ((((((((((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 - 11.0))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
}

Python

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

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 - 10.0) * 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 - 11.0))))))))) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
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 - 10.0) * ((((((((((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 - 11.0))))))))) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
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 - 10.0), $MachinePrecision] * 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 - 11.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

5. Applied rewrites 97.8%

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

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (- x 20.0)
   (*
    (- 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))))))))))))))
  (* (- x 19.0) (- x 18.0))))

C

double code(double x) {
	return ((x - 20.0) * ((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)))))))))))))) * ((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 = ((x - 20.0d0) * ((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 - 19.0d0) * (x - 18.0d0))
end function

Java

public static double code(double x) {
	return ((x - 20.0) * ((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)))))))))))))) * ((x - 19.0) * (x - 18.0));
}

Python

def code(x):
	return ((x - 20.0) * ((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)))))))))))))) * ((x - 19.0) * (x - 18.0))

Julia

function code(x)
	return Float64(Float64(Float64(x - 20.0) * 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 - 19.0) * Float64(x - 18.0)))
end

MATLAB

function tmp = code(x)
	tmp = ((x - 20.0) * ((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)))))))))))))) * ((x - 19.0) * (x - 18.0));
end

Wolfram

code[x_] := N[(N[(N[(x - 20.0), $MachinePrecision] * 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]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 10: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. lower-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 11: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 12: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (- x 1.0) (* (* (- x 3.0) (- x 2.0)) (- 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 - 3.0) * (x - 2.0)) * (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 - 3.0d0) * (x - 2.0d0)) * (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 - 3.0) * (x - 2.0)) * (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 - 3.0) * (x - 2.0)) * (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(x - 1.0) * Float64(Float64(Float64(x - 3.0) * Float64(x - 2.0)) * 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 - 3.0) * (x - 2.0)) * (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[(x - 1.0), $MachinePrecision] * N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*l* N/A

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

   5. associate-*l* N/A

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

   6. lower-*.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 13: 97.8% accurate, 1.0× speedup

Math

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

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 20.0) (- x 18.0)))
  (- x 19.0)))

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 - 20.0) * (x - 18.0))) * (x - 19.0);
}

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 - 20.0d0) * (x - 18.0d0))) * (x - 19.0d0)
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 - 20.0) * (x - 18.0))) * (x - 19.0);
}

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 - 20.0) * (x - 18.0))) * (x - 19.0)

Julia

function code(x)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 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(Float64(x - 20.0) * Float64(x - 18.0))) * Float64(x - 19.0))
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 - 20.0) * (x - 18.0))) * (x - 19.0);
end

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 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[(N[(x - 20.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

5. Applied rewrites 97.8%

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

Alternative 14: 28.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 9:\\ \;\;\;\;\left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 9.0)
   (*
    (*
     (- 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))))))))))))
    (+ 116280.0 (* x (- (* x (+ 2051.0 (* -74.0 x))) 25234.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (- (* x (+ 274.0 (* x (- (* 85.0 x) 225.0)))) 120.0)
                  (- x 6.0))
                 (- x 7.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 9.0) {
		tmp = ((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)))))))))))) * (116280.0 + (x * ((x * (2051.0 + (-74.0 * x))) - 25234.0)));
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 9.0d0) then
        tmp = ((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)))))))))))) * (116280.0d0 + (x * ((x * (2051.0d0 + ((-74.0d0) * x))) - 25234.0d0)))
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 9.0) {
		tmp = ((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)))))))))))) * (116280.0 + (x * ((x * (2051.0 + (-74.0 * x))) - 25234.0)));
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 9.0:
		tmp = ((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)))))))))))) * (116280.0 + (x * ((x * (2051.0 + (-74.0 * x))) - 25234.0)))
	else:
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 9.0)
		tmp = Float64(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(116280.0 + Float64(x * Float64(Float64(x * Float64(2051.0 + Float64(-74.0 * x))) - 25234.0))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 9.0)
		tmp = ((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)))))))))))) * (116280.0 + (x * ((x * (2051.0 + (-74.0 * x))) - 25234.0)));
	else
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 9.0], N[(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] * N[(116280.0 + N[(x * N[(N[(x * N[(2051.0 + N[(-74.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 25234.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + \color{blue}{x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \color{blue}{\left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - \color{blue}{25234}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)\right) \]

      6. lower-*.f64 24.1%

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)\right) \]

   6. Applied rewrites 24.1%

      \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(116280 + x \cdot \left(x \cdot \left(2051 + -74 \cdot x\right) - 25234\right)\right)} \]

   if 9 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - \color{blue}{120}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-*.f64 13.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 13.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 25.1% 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 97.8%

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

3. Applied rewrites 97.8%

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

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 25.1%

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

6. Applied rewrites 25.1%

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

Alternative 16: 25.1% accurate, 1.0× speedup

Math

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

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 2.0) (* (- x 1.0) (- x 3.0)))) (- 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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0d0) * ((x - 1.0d0) * (x - 3.0d0)))) * (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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0) * Float64(Float64(x - 1.0) * Float64(x - 3.0)))) * 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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(x - 3.0), $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 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. lower-*.f64 N/A

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

   10. lower-*.f64 97.8%

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

5. Applied rewrites 97.8%

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

6. Taylor expanded in x around 0

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

   1. lower--.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. lower-*.f64 25.1%

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

8. Applied rewrites 25.1%

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

Alternative 17: 23.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 9.2:\\ \;\;\;\;\left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(2051 \cdot x - 25234\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 9.2)
   (*
    (*
     (- 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))))))))))))
    (+ 116280.0 (* x (- (* 2051.0 x) 25234.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (- (* x (+ 274.0 (* x (- (* 85.0 x) 225.0)))) 120.0)
                  (- x 6.0))
                 (- x 7.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 9.2) {
		tmp = ((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)))))))))))) * (116280.0 + (x * ((2051.0 * x) - 25234.0)));
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 9.2d0) then
        tmp = ((x - 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)))))))))))) * (116280.0d0 + (x * ((2051.0d0 * x) - 25234.0d0)))
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 9.2) {
		tmp = ((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)))))))))))) * (116280.0 + (x * ((2051.0 * x) - 25234.0)));
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 9.2:
		tmp = ((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)))))))))))) * (116280.0 + (x * ((2051.0 * x) - 25234.0)))
	else:
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 9.2)
		tmp = Float64(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(116280.0 + Float64(x * Float64(Float64(2051.0 * x) - 25234.0))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 9.2)
		tmp = ((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)))))))))))) * (116280.0 + (x * ((2051.0 * x) - 25234.0)));
	else
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 9.2], N[(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] * N[(116280.0 + N[(x * N[(N[(2051.0 * x), $MachinePrecision] - 25234.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.1999999999999993

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(116280 + x \cdot \left(2051 \cdot x - 25234\right)\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + \color{blue}{x \cdot \left(2051 \cdot x - 25234\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \color{blue}{\left(2051 \cdot x - 25234\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(2051 \cdot x - \color{blue}{25234}\right)\right) \]

      4. lower-*.f64 21.8%

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + x \cdot \left(2051 \cdot x - 25234\right)\right) \]

   6. Applied rewrites 21.8%

      \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(116280 + x \cdot \left(2051 \cdot x - 25234\right)\right)} \]

   if 9.1999999999999993 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - \color{blue}{120}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-*.f64 13.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 13.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 21.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6.25:\\ \;\;\;\;\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(x - 8\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(1082 \cdot x - 6840\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 6.25)
   (*
    (*
     (- 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 4.0) (- x 5.0))
              (*
               (* (* (- x 3.0) (* (- x 2.0) (- x 1.0))) (- x 6.0))
               (* (- x 7.0) (- x 8.0)))))))))))))
    (- (* 1082.0 x) 6840.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (- (* x (+ 274.0 (* x (- (* 85.0 x) 225.0)))) 120.0)
                  (- x 6.0))
                 (- x 7.0))
                (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 6.25) {
		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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((1082.0 * x) - 6840.0);
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	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 <= 6.25d0) 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 - 4.0d0) * (x - 5.0d0)) * ((((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0))) * (x - 6.0d0)) * ((x - 7.0d0) * (x - 8.0d0))))))))))))) * ((1082.0d0 * x) - 6840.0d0)
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.25) {
		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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((1082.0 * x) - 6840.0);
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.25:
		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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((1082.0 * x) - 6840.0)
	else:
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.25)
		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(Float64(x - 4.0) * Float64(x - 5.0)) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0))) * Float64(x - 6.0)) * Float64(Float64(x - 7.0) * Float64(x - 8.0))))))))))))) * 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(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.25)
		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 - 4.0) * (x - 5.0)) * ((((x - 3.0) * ((x - 2.0) * (x - 1.0))) * (x - 6.0)) * ((x - 7.0) * (x - 8.0))))))))))))) * ((1082.0 * x) - 6840.0);
	else
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.25], 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[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(x - 8.0), $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[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.25

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 14.7%

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

   10. Applied rewrites 14.7%

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

   if 6.25 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - \color{blue}{120}\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-*.f64 13.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 13.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right)} \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 21.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 5.0)
   (*
    (*
     (- 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 2.0) (* (- x 1.0) (- x 3.0))))
                 (- x 5.0))
                (- x 6.0)))))))))))))
    (- (* 1082.0 x) 6840.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 11.0 x) 6.0) (- 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) {
	double tmp;
	if (x <= 5.0) {
		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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0);
	} else {
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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);
	}
	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 <= 5.0d0) 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 - 2.0d0) * ((x - 1.0d0) * (x - 3.0d0)))) * (x - 5.0d0)) * (x - 6.0d0))))))))))))) * ((1082.0d0 * x) - 6840.0d0)
    else
        tmp = ((((((((((((((((((11.0d0 * x) - 6.0d0) * (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 if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 5.0) {
		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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0);
	} else {
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 5.0:
		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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0)
	else:
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 5.0)
		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 - 2.0) * Float64(Float64(x - 1.0) * Float64(x - 3.0)))) * 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(Float64(11.0 * x) - 6.0) * 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
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 5.0)
		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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (x - 5.0)) * (x - 6.0))))))))))))) * ((1082.0 * x) - 6840.0);
	else
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 5.0], 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 - 2.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(x - 3.0), $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[(N[(11.0 * x), $MachinePrecision] - 6.0), $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]]

Derivation

1. Split input into 2 regimes

2. if x < 5

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 97.8%

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 14.7%

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

   8. Applied rewrites 14.7%

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

   if 5 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 15.0%

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

   4. Applied rewrites 15.0%

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

Alternative 20: 20.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.2:\\ \;\;\;\;\left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + -25234 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.2)
   (*
    (*
     (- 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))))))))))))
    (+ 116280.0 (* -25234.0 x)))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 11.0 x) 6.0) (- 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) {
	double tmp;
	if (x <= 4.2) {
		tmp = ((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)))))))))))) * (116280.0 + (-25234.0 * x));
	} else {
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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);
	}
	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 <= 4.2d0) then
        tmp = ((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)))))))))))) * (116280.0d0 + ((-25234.0d0) * x))
    else
        tmp = ((((((((((((((((((11.0d0 * x) - 6.0d0) * (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 if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 4.2) {
		tmp = ((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)))))))))))) * (116280.0 + (-25234.0 * x));
	} else {
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.2:
		tmp = ((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)))))))))))) * (116280.0 + (-25234.0 * x))
	else:
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.2)
		tmp = Float64(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(116280.0 + Float64(-25234.0 * x)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(11.0 * x) - 6.0) * 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
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 4.2)
		tmp = ((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)))))))))))) * (116280.0 + (-25234.0 * x));
	else
		tmp = ((((((((((((((((((11.0 * x) - 6.0) * (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
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.2], N[(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] * N[(116280.0 + N[(-25234.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(11.0 * x), $MachinePrecision] - 6.0), $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]]

Derivation

1. Split input into 2 regimes

2. if x < 4.20000000000000018

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(116280 + -25234 \cdot x\right)} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + \color{blue}{-25234 \cdot x}\right) \]

      2. lower-*.f64 12.1%

         \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(116280 + -25234 \cdot \color{blue}{x}\right) \]

   6. Applied rewrites 12.1%

      \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(116280 + -25234 \cdot x\right)} \]

   if 4.20000000000000018 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 15.0%

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

   4. Applied rewrites 15.0%

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

Alternative 21: 17.9% accurate, 1.1× speedup

Math

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

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 2.0) (* (- x 1.0) (- x 3.0)))) (- 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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0d0) * ((x - 1.0d0) * (x - 3.0d0)))) * (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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0) * Float64(Float64(x - 1.0) * Float64(x - 3.0)))) * 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 - 2.0) * ((x - 1.0) * (x - 3.0)))) * (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 - 2.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(x - 3.0), $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 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. lower-*.f64 N/A

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

   10. lower-*.f64 97.8%

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

5. Applied rewrites 97.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 17.9%

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

Alternative 22: 17.0% accurate, 1.2× speedup

Math

\[\left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot 116280 \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (- 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))))))))))))
  116280.0))

C

double code(double x) {
	return ((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)))))))))))) * 116280.0;
}

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 - 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)))))))))))) * 116280.0d0
end function

Java

public static double code(double x) {
	return ((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)))))))))))) * 116280.0;
}

Python

def code(x):
	return ((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)))))))))))) * 116280.0

Julia

function code(x)
	return Float64(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)))))))))))) * 116280.0)
end

MATLAB

function tmp = code(x)
	tmp = ((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)))))))))))) * 116280.0;
end

Wolfram

code[x_] := N[(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] * 116280.0), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

4. Taylor expanded in x around 0

   \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{116280} \]
5. Step-by-step derivation

6. Applied rewrites 17.0%

   \[\leadsto \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(x - 12\right) \cdot \left(\left(x - 11\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(x - 9\right) \cdot \left(\left(x - 8\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(\left(x - 4\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{116280} \]
7. Add Preprocessing

Alternative 23: 15.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{7} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot -17\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (pow x 7.0) (- x 8.0)) (- x 9.0)) (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (* 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))
       -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)) <= -10000000000000.0) {
		tmp = ((((((((((((pow(x, 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((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)) * -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)) <= (-10000000000000.0d0)) then
        tmp = (((((((((((((x ** 7.0d0) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((((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)) * (-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)) <= -10000000000000.0) {
		tmp = ((((((((((((Math.pow(x, 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((((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)) * -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)) <= -10000000000000.0:
		tmp = ((((((((((((math.pow(x, 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((((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)) * -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)) <= -10000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 7.0) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) * -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)) <= -10000000000000.0)
		tmp = (((((((((((((x ^ 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((((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)) * -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], -10000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 7.0], $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(24.0 * 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] * -17.0), $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))) < -1e13

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 12.1%

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

   4. Applied rewrites 12.1%

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

   if -1e13 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 10.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 10.1%

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

Alternative 24: 15.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot -17\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 9.0) (+ 1925.0 (* -66.0 x))) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (* 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))
       -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)) <= -10000000000000.0) {
		tmp = (((((((((pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= (-10000000000000.0d0)) then
        tmp = ((((((((((x ** 9.0d0) * (1925.0d0 + ((-66.0d0) * x))) * (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 = (((((((((((((((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)) * (-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)) <= -10000000000000.0) {
		tmp = (((((((((Math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= -10000000000000.0:
		tmp = (((((((((math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= -10000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(1925.0 + Float64(-66.0 * x))) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) * -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)) <= -10000000000000.0)
		tmp = ((((((((((x ^ 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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], -10000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 9.0], $MachinePrecision] * N[(1925.0 + N[(-66.0 * x), $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[(N[(N[(N[(N[(24.0 * 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] * -17.0), $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))) < -1e13

   1. Initial program 97.8%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \color{blue}{\left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \color{blue}{\left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(\color{blue}{-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x}} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - \color{blue}{1}\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lower-/.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66 \cdot x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66} \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot \color{blue}{x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 10.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 10.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -1e13 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 10.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 10.1%

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

Alternative 25: 15.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot -16\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 9.0) (+ 1925.0 (* -66.0 x))) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (* 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))
        -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)) <= -10000000000000.0) {
		tmp = (((((((((pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= (-10000000000000.0d0)) then
        tmp = ((((((((((x ** 9.0d0) * (1925.0d0 + ((-66.0d0) * x))) * (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 = (((((((((((((((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)) * (-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)) <= -10000000000000.0) {
		tmp = (((((((((Math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= -10000000000000.0:
		tmp = (((((((((math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= -10000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(1925.0 + Float64(-66.0 * x))) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) * -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)) <= -10000000000000.0)
		tmp = ((((((((((x ^ 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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], -10000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 9.0], $MachinePrecision] * N[(1925.0 + N[(-66.0 * x), $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[(N[(N[(N[(N[(24.0 * 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] * -16.0), $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))) < -1e13

   1. Initial program 97.8%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \color{blue}{\left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \color{blue}{\left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(\color{blue}{-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x}} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - \color{blue}{1}\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lower-/.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66 \cdot x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66} \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot \color{blue}{x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 10.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 10.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -1e13 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 10.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 10.0%

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

Alternative 26: 14.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot -15\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -5000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 9.0) (+ 1925.0 (* -66.0 x))) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (* 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))
         -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)) <= -5000000000000.0) {
		tmp = (((((((((pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= (-5000000000000.0d0)) then
        tmp = ((((((((((x ** 9.0d0) * (1925.0d0 + ((-66.0d0) * x))) * (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 = (((((((((((((((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)) * (-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)) <= -5000000000000.0) {
		tmp = (((((((((Math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= -5000000000000.0:
		tmp = (((((((((math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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)) <= -5000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(1925.0 + Float64(-66.0 * x))) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) * -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)) <= -5000000000000.0)
		tmp = ((((((((((x ^ 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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 = (((((((((((((((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)) * -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], -5000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 9.0], $MachinePrecision] * N[(1925.0 + N[(-66.0 * x), $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[(N[(N[(N[(N[(24.0 * 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] * -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]]

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))) < -5e12

   1. Initial program 97.8%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \color{blue}{\left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \color{blue}{\left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(\color{blue}{-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x}} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - \color{blue}{1}\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lower-/.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66 \cdot x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66} \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot \color{blue}{x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 10.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 10.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 10.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 9.6%

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

Alternative 27: 14.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 1000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      1000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (* (* (- (* 13068.0 x) 5040.0) (- x 8.0)) (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 1000000000000.0) {
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 1000000000000.0d0) then
        tmp = ((((((((((((((13068.0d0 * x) - 5040.0d0) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 1000000000000.0) {
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 1000000000000.0:
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 1000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(13068.0 * x) - 5040.0) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 1000000000000.0)
		tmp = ((((((((((((((13068.0 * x) - 5040.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 1000000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(13068.0 * x), $MachinePrecision] - 5040.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(13068 \cdot x - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - \color{blue}{5040}\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 11.5%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 11.5%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(13068 \cdot x - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 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 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.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 28: 14.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 415000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      415000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (* (pow x 9.0) (- x 10.0)) (- x 11.0)) (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0) {
		tmp = ((((((((((pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 415000000000.0d0) then
        tmp = (((((((((((x ** 9.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0) {
		tmp = ((((((((((Math.pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0:
		tmp = ((((((((((math.pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 415000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0)
		tmp = (((((((((((x ^ 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 415000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 9.0], $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 4.15e11

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 10.8%

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

   4. Applied rewrites 10.8%

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

   if 4.15e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.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 29: 14.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 9.0) (+ 1925.0 (* -66.0 x))) (- x 12.0)) (- 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)) <= -10000000000.0) {
		tmp = (((((((((pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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)) <= (-10000000000.0d0)) then
        tmp = ((((((((((x ** 9.0d0) * (1925.0d0 + ((-66.0d0) * x))) * (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)) <= -10000000000.0) {
		tmp = (((((((((Math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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)) <= -10000000000.0:
		tmp = (((((((((math.pow(x, 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(1925.0 + Float64(-66.0 * x))) * 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)) <= -10000000000.0)
		tmp = ((((((((((x ^ 9.0) * (1925.0 + (-66.0 * x))) * (x - 12.0)) * (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], -10000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 9.0], $MachinePrecision] * N[(1925.0 + N[(-66.0 * x), $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[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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \color{blue}{\left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \color{blue}{\left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(\color{blue}{-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x}} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - \color{blue}{1}\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lower-/.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66 \cdot x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + \color{blue}{-66} \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot \color{blue}{x}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 10.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(1925 + -66 \cdot x\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 10.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \color{blue}{\left(1925 + -66 \cdot x\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.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 30: 14.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot {x}^{9}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* (* 1925.0 (pow x 9.0)) (- x 12.0)) (- 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)) <= -10000000000.0) {
		tmp = (((((((((1925.0 * pow(x, 9.0)) * (x - 12.0)) * (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)) <= (-10000000000.0d0)) then
        tmp = (((((((((1925.0d0 * (x ** 9.0d0)) * (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)) <= -10000000000.0) {
		tmp = (((((((((1925.0 * Math.pow(x, 9.0)) * (x - 12.0)) * (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)) <= -10000000000.0:
		tmp = (((((((((1925.0 * math.pow(x, 9.0)) * (x - 12.0)) * (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)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1925.0 * (x ^ 9.0)) * 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)) <= -10000000000.0)
		tmp = (((((((((1925.0 * (x ^ 9.0)) * (x - 12.0)) * (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], -10000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1925.0 * N[Power[x, 9.0], $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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \color{blue}{\left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \color{blue}{\left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(\color{blue}{-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x}} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - \color{blue}{1}\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lower-/.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot \color{blue}{{x}^{9}}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot {x}^{\color{blue}{9}}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot {x}^{9}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot \color{blue}{{x}^{9}}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.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 31: 13.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot {x}^{9}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{12} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* (* 1925.0 (pow x 9.0)) (- x 12.0)) (- x 13.0)) (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* (pow x 12.0) (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = (((((((((1925.0 * pow(x, 9.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 100000000000.0d0) then
        tmp = (((((((((1925.0d0 * (x ** 9.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((x ** 12.0d0) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = (((((((((1925.0 * Math.pow(x, 9.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((Math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0:
		tmp = (((((((((1925.0 * math.pow(x, 9.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1925.0 * (x ^ 9.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 12.0) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0)
		tmp = (((((((((1925.0 * (x ^ 9.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((x ^ 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1925.0 * N[Power[x, 9.0], $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 12.0], $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 1e11

   1. Initial program 97.8%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \color{blue}{\left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \color{blue}{\left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)}\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(\color{blue}{-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x}} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - \color{blue}{1}\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      9. lower-/.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(-1 \cdot \left({x}^{11} \cdot \left(-1 \cdot \frac{1925 \cdot \frac{1}{x} - 66}{x} - 1\right)\right)\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot \color{blue}{{x}^{9}}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot {x}^{\color{blue}{9}}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot {x}^{9}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(1925 \cdot \color{blue}{{x}^{9}}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.3%

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

   4. Applied rewrites 7.3%

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

Alternative 32: 13.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 415000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{12} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      415000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 1026576.0 x) 362880.0) (- x 10.0)) (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* (pow x 12.0) (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 415000000000.0d0) then
        tmp = ((((((((((((1026576.0d0 * x) - 362880.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((x ** 12.0d0) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((Math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0:
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 415000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1026576.0 * x) - 362880.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 12.0) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 415000000000.0)
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((x ^ 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 415000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1026576.0 * x), $MachinePrecision] - 362880.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 12.0], $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 4.15e11

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.8%

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

   4. Applied rewrites 10.8%

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

   if 4.15e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.3%

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

   4. Applied rewrites 7.3%

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

Alternative 33: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{12} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (- (* 120543840.0 x) 39916800.0) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* (pow x 12.0) (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 100000000000.0d0) then
        tmp = ((((((((((120543840.0d0 * x) - 39916800.0d0) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((x ** 12.0d0) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((Math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0:
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((math.pow(x, 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(120543840.0 * x) - 39916800.0) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 12.0) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 100000000000.0)
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((x ^ 12.0) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(120543840.0 * x), $MachinePrecision] - 39916800.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 12.0], $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 1e11

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - \color{blue}{39916800}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.3%

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

   4. Applied rewrites 7.3%

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

Alternative 34: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 100000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      100000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (- (* 120543840.0 x) 39916800.0) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* (* 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)) <= 100000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((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)) <= 100000000000.0d0) then
        tmp = ((((((((((120543840.0d0 * x) - 39916800.0d0) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((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)) <= 100000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((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)) <= 100000000000.0:
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((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)) <= 100000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(120543840.0 * x) - 39916800.0) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) <= 100000000000.0)
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((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], 100000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(120543840.0 * x), $MachinePrecision] - 39916800.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(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))) < 1e11

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - \color{blue}{39916800}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if 1e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 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 35: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -10000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (- (* 120543840.0 x) 39916800.0) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (* (* (* (* 479001600.0 (- x 13.0)) (- x 14.0)) (- x 15.0)) (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -10000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-10000000000.0d0)) then
        tmp = ((((((((((120543840.0d0 * x) - 39916800.0d0) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((479001600.0d0 * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -10000000000.0) {
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -10000000000.0:
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(120543840.0 * x) - 39916800.0) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(479001600.0 * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -10000000000.0)
		tmp = ((((((((((120543840.0 * x) - 39916800.0) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((479001600.0 * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -10000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(120543840.0 * x), $MachinePrecision] - 39916800.0), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(479001600.0 * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - \color{blue}{39916800}\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 10.2%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 10.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(120543840 \cdot x - 39916800\right)} \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 7.3%

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

Alternative 36: 13.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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)) <= -10000000000.0) {
		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)) <= (-10000000000.0d0)) 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)) <= -10000000000.0) {
		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)) <= -10000000000.0:
		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)) <= -10000000000.0)
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.6%

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

   4. Applied rewrites 9.6%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\color{blue}{479001600} \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 7.3%

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

Alternative 37: 13.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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)) <= -10000000000.0) {
		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)) <= (-10000000000.0d0)) 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)) <= -10000000000.0) {
		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)) <= -10000000000.0:
		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)) <= -10000000000.0)
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.6%

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

   4. Applied rewrites 9.6%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.8%

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

Alternative 38: 13.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(87178291200 \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (*
     (*
      (* (* (- (* 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)) <= -10000000000.0) {
		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)) <= (-10000000000.0d0)) 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)) <= -10000000000.0) {
		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)) <= -10000000000.0:
		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)) <= -10000000000.0)
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.0%

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

   4. Applied rewrites 9.0%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{87178291200} \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.8%

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

Alternative 39: 12.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(4339163001600 \cdot x - 1307674368000\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(13566 \cdot {x}^{16}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (*
     (*
      (* (* (- (* 4339163001600.0 x) 1307674368000.0) (- x 16.0)) (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (* (* (* 13566.0 (pow x 16.0)) (- 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)) <= -10000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((13566.0 * pow(x, 16.0)) * (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)) <= (-10000000000.0d0)) then
        tmp = ((((((4339163001600.0d0 * x) - 1307674368000.0d0) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((13566.0d0 * (x ** 16.0d0)) * (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)) <= -10000000000.0) {
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((13566.0 * Math.pow(x, 16.0)) * (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)) <= -10000000000.0:
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((13566.0 * math.pow(x, 16.0)) * (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)) <= -10000000000.0)
		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(13566.0 * (x ^ 16.0)) * 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)) <= -10000000000.0)
		tmp = ((((((4339163001600.0 * x) - 1307674368000.0) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((13566.0 * (x ^ 16.0)) * (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], -10000000000.0], 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[(13566.0 * N[Power[x, 16.0], $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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(4339163001600 \cdot x - 1307674368000\right)} \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.0%

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

   4. Applied rewrites 9.0%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \color{blue}{\left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\color{blue}{\left(1 + \frac{13566}{{x}^{2}}\right)} - 171 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - \color{blue}{171 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-+.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - \color{blue}{171} \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-pow.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-/.f64 5.9%

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 5.9%

      \[\leadsto \left(\color{blue}{\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(13566 \cdot \color{blue}{{x}^{16}}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(13566 \cdot {x}^{\color{blue}{16}}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 5.9%

         \[\leadsto \left(\left(13566 \cdot {x}^{16}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 5.9%

      \[\leadsto \left(\left(13566 \cdot \color{blue}{{x}^{16}}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 40: 12.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(13566 \cdot {x}^{16}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (- (* 1223405590579200.0 x) 355687428096000.0)
    (* (- x 18.0) (* (- x 20.0) (- x 19.0))))
   (* (* (* 13566.0 (pow x 16.0)) (- 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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} else {
		tmp = ((13566.0 * pow(x, 16.0)) * (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)) <= (-10000000000.0d0)) then
        tmp = ((1223405590579200.0d0 * x) - 355687428096000.0d0) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
    else
        tmp = ((13566.0d0 * (x ** 16.0d0)) * (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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} else {
		tmp = ((13566.0 * Math.pow(x, 16.0)) * (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)) <= -10000000000.0:
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))
	else:
		tmp = ((13566.0 * math.pow(x, 16.0)) * (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)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	else
		tmp = Float64(Float64(Float64(13566.0 * (x ^ 16.0)) * 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)) <= -10000000000.0)
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	else
		tmp = ((13566.0 * (x ^ 16.0)) * (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], -10000000000.0], N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(13566.0 * N[Power[x, 16.0], $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))) < -1e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.6%

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

   6. Applied rewrites 8.6%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \color{blue}{\left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\color{blue}{\left(1 + \frac{13566}{{x}^{2}}\right)} - 171 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - \color{blue}{171 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-+.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - \color{blue}{171} \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-pow.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-/.f64 5.9%

         \[\leadsto \left(\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 5.9%

      \[\leadsto \left(\color{blue}{\left({x}^{18} \cdot \left(\left(1 + \frac{13566}{{x}^{2}}\right) - 171 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(13566 \cdot \color{blue}{{x}^{16}}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(13566 \cdot {x}^{\color{blue}{16}}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 5.9%

         \[\leadsto \left(\left(13566 \cdot {x}^{16}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 5.9%

      \[\leadsto \left(\left(13566 \cdot \color{blue}{{x}^{16}}\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 41: 12.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left({x}^{18} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (- (* 1223405590579200.0 x) 355687428096000.0)
    (* (- x 18.0) (* (- x 20.0) (- x 19.0))))
   (* (* (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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} 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)) <= (-10000000000.0d0)) then
        tmp = ((1223405590579200.0d0 * x) - 355687428096000.0d0) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} 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)) <= -10000000000.0:
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))
	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)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) <= -10000000000.0)
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	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], -10000000000.0], N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $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))) < -1e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.6%

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

   6. Applied rewrites 8.6%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 5.9%

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

   4. Applied rewrites 5.9%

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

Alternative 42: 12.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(20922789888000 \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (- (* 1223405590579200.0 x) 355687428096000.0)
    (* (- x 18.0) (* (- x 20.0) (- x 19.0))))
   (*
    (* (* (* 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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} 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)) <= (-10000000000.0d0)) then
        tmp = ((1223405590579200.0d0 * x) - 355687428096000.0d0) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} 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)) <= -10000000000.0:
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))
	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)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) <= -10000000000.0)
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	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], -10000000000.0], N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $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))) < -1e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.6%

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

   6. Applied rewrites 8.6%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.3%

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

Alternative 43: 12.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

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))
      -10000000000.0)
   (*
    (- (* 1223405590579200.0 x) 355687428096000.0)
    (* (- x 18.0) (* (- x 20.0) (- x 19.0))))
   (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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} 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)) <= (-10000000000.0d0)) then
        tmp = ((1223405590579200.0d0 * x) - 355687428096000.0d0) * ((x - 18.0d0) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) <= -10000000000.0) {
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	} 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)) <= -10000000000.0:
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)))
	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)) <= -10000000000.0)
		tmp = Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) <= -10000000000.0)
		tmp = ((1223405590579200.0 * x) - 355687428096000.0) * ((x - 18.0) * ((x - 20.0) * (x - 19.0)));
	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], -10000000000.0], N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $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))) < -1e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.6%

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

   6. Applied rewrites 8.6%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{20}} \]
   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 44: 12.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

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))
      -10000000000.0)
   (* (- (* 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)) <= -10000000000.0) {
		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)) <= (-10000000000.0d0)) 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)) <= -10000000000.0) {
		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)) <= -10000000000.0:
		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)) <= -10000000000.0)
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.2%

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

   4. Applied rewrites 8.2%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{20}} \]
   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 45: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (* (- (* 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)) <= -10000000000.0) {
		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)) <= (-10000000000.0d0)) 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)) <= -10000000000.0) {
		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)) <= -10000000000.0:
		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)) <= -10000000000.0)
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.2%

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

   4. Applied rewrites 8.2%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 6.0%

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

Alternative 46: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (* (- (* 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)) <= -10000000000.0) {
		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)) <= (-10000000000.0d0)) 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)) <= -10000000000.0) {
		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)) <= -10000000000.0:
		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)) <= -10000000000.0)
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.2%

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

   4. Applied rewrites 8.2%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.6%

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

Alternative 47: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -10000000000.0)
   (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)) <= -10000000000.0) {
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.1%

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

   8. Applied rewrites 8.1%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto -8752948036761600000 \cdot x + \color{blue}{2432902008176640000} \]

      3. lift-*.f64 N/A

         \[\leadsto -8752948036761600000 \cdot x + 2432902008176640000 \]

      4. *-commutative N/A

         \[\leadsto x \cdot -8752948036761600000 + 2432902008176640000 \]

      5. lower-fma.f64 8.1%

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

   10. Applied rewrites 8.1%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.6%

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

Alternative 48: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -10000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

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))
      -10000000000.0)
   (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)) <= -10000000000.0) {
		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)) <= -10000000000.0)
		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], -10000000000.0], 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))) < -1e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

   5. Applied rewrites 97.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.1%

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

   8. Applied rewrites 8.1%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto -8752948036761600000 \cdot x + \color{blue}{2432902008176640000} \]

      3. lift-*.f64 N/A

         \[\leadsto -8752948036761600000 \cdot x + 2432902008176640000 \]

      4. *-commutative N/A

         \[\leadsto x \cdot -8752948036761600000 + 2432902008176640000 \]

      5. lower-fma.f64 8.1%

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

   10. Applied rewrites 8.1%

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

   if -1e10 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.6%

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

Alternative 49: 5.6% accurate, 109.5× speedup

Math

\[2.43290200817664 \cdot 10^{+18} \]

FPCore

(FPCore (x) :precision binary64 2.43290200817664e+18)

C

double code(double x) {
	return 2.43290200817664e+18;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = 2.43290200817664d+18
end function

Java

public static double code(double x) {
	return 2.43290200817664e+18;
}

Python

def code(x):
	return 2.43290200817664e+18

Julia

function code(x)
	return 2.43290200817664e+18
end

MATLAB

function tmp = code(x)
	tmp = 2.43290200817664e+18;
end

Wolfram

code[x_] := 2.43290200817664e+18

Derivation

1. Initial program 97.8%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 5.6%

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

Reproduce

herbie shell --seed 2025187 
(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)))