(x - 1) to (x - 20)

Percentage Accurate: 97.8% → 98.0%

Time: 19.7s

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: 98.0% accurate, 1.0× speedup

Math

\[\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \mathsf{fma}\left(x, -12, 132\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (- x 18.0)
  (*
   (*
    (- x 17.0)
    (*
     (- x 16.0)
     (*
      (- x 15.0)
      (*
       (- x 14.0)
       (*
        (- x 13.0)
        (*
         (fma (- x 11.0) x (fma x -12.0 132.0))
         (*
          (- x 10.0)
          (*
           (* (- x 9.0) (- x 8.0))
           (*
            (- x 7.0)
            (*
             (* (- x 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
             (* (- x 5.0) (- x 4.0))))))))))))
   (* (- x 20.0) (- x 19.0)))))

C

double code(double x) {
	return (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * (fma((x - 11.0), x, fma(x, -12.0, 132.0)) * ((x - 10.0) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)));
}

Julia

function code(x)
	return Float64(Float64(x - 18.0) * 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(fma(Float64(x - 11.0), x, fma(x, -12.0, 132.0)) * Float64(Float64(x - 10.0) * Float64(Float64(Float64(x - 9.0) * Float64(x - 8.0)) * Float64(Float64(x - 7.0) * Float64(Float64(Float64(x - 6.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(Float64(x - 5.0) * Float64(x - 4.0)))))))))))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
end

Wolfram

code[x_] := N[(N[(x - 18.0), $MachinePrecision] * 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[(N[(x - 11.0), $MachinePrecision] * x + N[(x * -12.0 + 132.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \mathsf{fma}\left(x, -12, \color{blue}{132}\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

7. Applied rewrites 98.0%

   \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \color{blue}{\mathsf{fma}\left(x, -12, 132\right)}\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
8. Add Preprocessing

Alternative 2: 98.0% accurate, 1.0× speedup

Math

\[\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(\left(\mathsf{fma}\left(x, \left(x - 11\right) + -12, 132\right) \cdot \left(x - 13\right)\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (- x 18.0)
  (*
   (*
    (- x 17.0)
    (*
     (- x 16.0)
     (*
      (- x 15.0)
      (*
       (- x 14.0)
       (*
        (*
         (* (fma x (+ (- x 11.0) -12.0) 132.0) (- x 13.0))
         (* (* (- x 9.0) (- x 10.0)) (- x 8.0)))
        (*
         (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
         (* (- x 6.0) (* (- x 3.0) (* (- x 1.0) (- x 2.0))))))))))
   (* (- x 20.0) (- x 19.0)))))

C

double code(double x) {
	return (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * (((fma(x, ((x - 11.0) + -12.0), 132.0) * (x - 13.0)) * (((x - 9.0) * (x - 10.0)) * (x - 8.0))) * (((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((x - 6.0) * ((x - 3.0) * ((x - 1.0) * (x - 2.0)))))))))) * ((x - 20.0) * (x - 19.0)));
}

Julia

function code(x)
	return Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(Float64(fma(x, Float64(Float64(x - 11.0) + -12.0), 132.0) * Float64(x - 13.0)) * Float64(Float64(Float64(x - 9.0) * Float64(x - 10.0)) * Float64(x - 8.0))) * Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(x - 6.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 1.0) * Float64(x - 2.0)))))))))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
end

Wolfram

code[x_] := N[(N[(x - 18.0), $MachinePrecision] * 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[(N[(N[(x * N[(N[(x - 11.0), $MachinePrecision] + -12.0), $MachinePrecision] + 132.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 9.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \mathsf{fma}\left(x, -12, \color{blue}{132}\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

7. Applied rewrites 98.0%

   \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \color{blue}{\mathsf{fma}\left(x, -12, 132\right)}\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

9. Applied rewrites 98.0%

   \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \left(x - 11\right) + -12, 132\right) \cdot \left(x - 13\right)\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 8\right)\right)\right) \cdot \left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)\right)\right)\right)}\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
10. Add Preprocessing

Alternative 3: 98.0% accurate, 1.0× speedup

Math

\[\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(\left(\left(\mathsf{fma}\left(x, \left(x - 11\right) + -12, 132\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 15\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (- x 18.0)
  (*
   (*
    (- x 17.0)
    (*
     (- x 16.0)
     (*
      (- x 14.0)
      (*
       (*
        (* (* (fma x (+ (- x 11.0) -12.0) 132.0) (- x 13.0)) (- x 10.0))
        (*
         (*
          (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
          (* (- x 6.0) (* (- x 3.0) (* (- x 1.0) (- x 2.0)))))
         (* (- x 8.0) (- x 9.0))))
       (- x 15.0)))))
   (* (- x 20.0) (- x 19.0)))))

C

double code(double x) {
	return (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 14.0) * ((((fma(x, ((x - 11.0) + -12.0), 132.0) * (x - 13.0)) * (x - 10.0)) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((x - 6.0) * ((x - 3.0) * ((x - 1.0) * (x - 2.0))))) * ((x - 8.0) * (x - 9.0)))) * (x - 15.0))))) * ((x - 20.0) * (x - 19.0)));
}

Julia

function code(x)
	return Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 14.0) * Float64(Float64(Float64(Float64(fma(x, Float64(Float64(x - 11.0) + -12.0), 132.0) * Float64(x - 13.0)) * Float64(x - 10.0)) * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(x - 6.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 1.0) * Float64(x - 2.0))))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 15.0))))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))))
end

Wolfram

code[x_] := N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(N[(N[(N[(x * N[(N[(x - 11.0), $MachinePrecision] + -12.0), $MachinePrecision] + 132.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \mathsf{fma}\left(x, -12, \color{blue}{132}\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

7. Applied rewrites 98.0%

   \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \color{blue}{\mathsf{fma}\left(x, -12, 132\right)}\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

9. Applied rewrites 98.0%

   \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \color{blue}{\left(\left(x - 14\right) \cdot \left(\left(\left(\left(\mathsf{fma}\left(x, \left(x - 11\right) + -12, 132\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 15\right)\right)\right)}\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
10. Add Preprocessing

Alternative 4: 98.0% accurate, 1.0× speedup

Math

\[\left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(\left(\left(\left(\left(\left(\left(\mathsf{fma}\left(x, \left(x - 11\right) + -12, 132\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right)\right)\right) \cdot \left(x - 19\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (- x 18.0)
   (*
    (- x 20.0)
    (*
     (*
      (*
       (*
        (*
         (* (* (fma x (+ (- x 11.0) -12.0) 132.0) (- x 13.0)) (- x 10.0))
         (*
          (*
           (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
           (* (- x 6.0) (* (- x 3.0) (* (- x 1.0) (- x 2.0)))))
          (* (- x 8.0) (- x 9.0))))
        (- x 14.0))
       (- x 15.0))
      (- x 16.0))
     (- x 17.0))))
  (- x 19.0)))

C

double code(double x) {
	return ((x - 18.0) * ((x - 20.0) * (((((((fma(x, ((x - 11.0) + -12.0), 132.0) * (x - 13.0)) * (x - 10.0)) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((x - 6.0) * ((x - 3.0) * ((x - 1.0) * (x - 2.0))))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)))) * (x - 19.0);
}

Julia

function code(x)
	return Float64(Float64(Float64(x - 18.0) * Float64(Float64(x - 20.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(fma(x, Float64(Float64(x - 11.0) + -12.0), 132.0) * Float64(x - 13.0)) * Float64(x - 10.0)) * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(x - 6.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 1.0) * Float64(x - 2.0))))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)))) * Float64(x - 19.0))
end

Wolfram

code[x_] := N[(N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * N[(N[(x - 11.0), $MachinePrecision] + -12.0), $MachinePrecision] + 132.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \mathsf{fma}\left(x, -12, \color{blue}{132}\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

7. Applied rewrites 98.0%

   \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\mathsf{fma}\left(x - 11, x, \color{blue}{\mathsf{fma}\left(x, -12, 132\right)}\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

9. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\left(\left(x - 18\right) \cdot \left(\left(x - 20\right) \cdot \left(\left(\left(\left(\left(\left(\left(\mathsf{fma}\left(x, \left(x - 11\right) + -12, 132\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 1\right) \cdot \left(x - 2\right)\right)\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right)\right)\right) \cdot \left(x - 19\right)} \]
10. Add Preprocessing

Alternative 5: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (- x 18.0)
  (*
   (*
    (- 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 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
             (* (- x 5.0) (- x 4.0))))))))))))
   (* (- x 20.0) (- x 19.0)))))

C

double code(double x) {
	return (x - 18.0) * (((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((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 - 18.0d0) * (((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 - 6.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * ((x - 5.0d0) * (x - 4.0d0)))))))))))) * ((x - 20.0d0) * (x - 19.0d0)))
end function

Java

public static double code(double x) {
	return (x - 18.0) * (((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)));
}

Python

def code(x):
	return (x - 18.0) * (((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)))

Julia

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

MATLAB

function tmp = code(x)
	tmp = (x - 18.0) * (((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)));
end

Wolfram

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

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

Alternative 6: 97.8% accurate, 1.0× speedup

Math

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

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 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
            (* (- x 5.0) (- x 4.0)))))))))))
   (* (* (- x 18.0) (- x 17.0)) (- x 19.0)))
  (- x 20.0)))

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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))) * (((x - 18.0) * (x - 17.0)) * (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 - 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 - 6.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * ((x - 5.0d0) * (x - 4.0d0))))))))))) * (((x - 18.0d0) * (x - 17.0d0)) * (x - 19.0d0))) * (x - 20.0d0)
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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))) * (((x - 18.0) * (x - 17.0)) * (x - 19.0))) * (x - 20.0);
}

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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))) * (((x - 18.0) * (x - 17.0)) * (x - 19.0))) * (x - 20.0)

Julia

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (- x 19.0)
  (*
   (*
    (- x 18.0)
    (*
     (- 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 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
              (* (- x 5.0) (- x 4.0)))))))))))))
   (- x 20.0))))

C

double code(double x) {
	return (x - 19.0) * (((x - 18.0) * ((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))))) * (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 - 19.0d0) * (((x - 18.0d0) * ((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 - 6.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * ((x - 5.0d0) * (x - 4.0d0))))))))))))) * (x - 20.0d0))
end function

Java

public static double code(double x) {
	return (x - 19.0) * (((x - 18.0) * ((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))))) * (x - 20.0));
}

Python

def code(x):
	return (x - 19.0) * (((x - 18.0) * ((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))))) * (x - 20.0))

Julia

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

MATLAB

function tmp = code(x)
	tmp = (x - 19.0) * (((x - 18.0) * ((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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0))))))))))))) * (x - 20.0));
end

Wolfram

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

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

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

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 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
              (* (- x 5.0) (- x 4.0))))))))))
      (- x 17.0)))
    (- x 18.0))
   (- x 19.0))
  (- x 20.0)))

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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))) * (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 - 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 - 6.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * ((x - 5.0d0) * (x - 4.0d0)))))))))) * (x - 17.0d0))) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))) * (x - 17.0))) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))) * (x - 17.0))) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)

Julia

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

MATLAB

function tmp = code(x)
	tmp = ((((x - 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 - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))))) * (x - 17.0))) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
end

Wolfram

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

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%

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

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (*
  (*
   (*
    (*
     (*
      (*
       (- x 14.0)
       (*
        (*
         (- x 13.0)
         (*
          (* (- x 12.0) (- x 11.0))
          (*
           (- x 10.0)
           (*
            (* (- x 9.0) (- x 8.0))
            (*
             (- x 7.0)
             (*
              (* (- x 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
              (* (- x 5.0) (- x 4.0))))))))
        (- 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 - 14.0) * (((x - 13.0) * (((x - 12.0) * (x - 11.0)) * ((x - 10.0) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))) * (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 - 14.0d0) * (((x - 13.0d0) * (((x - 12.0d0) * (x - 11.0d0)) * ((x - 10.0d0) * (((x - 9.0d0) * (x - 8.0d0)) * ((x - 7.0d0) * (((x - 6.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * ((x - 5.0d0) * (x - 4.0d0)))))))) * (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 - 14.0) * (((x - 13.0) * (((x - 12.0) * (x - 11.0)) * ((x - 10.0) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))) * (x - 15.0))) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
}

Python

def code(x):
	return ((((((x - 14.0) * (((x - 13.0) * (((x - 12.0) * (x - 11.0)) * ((x - 10.0) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))) * (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(x - 14.0) * Float64(Float64(Float64(x - 13.0) * Float64(Float64(Float64(x - 12.0) * Float64(x - 11.0)) * Float64(Float64(x - 10.0) * Float64(Float64(Float64(x - 9.0) * Float64(x - 8.0)) * Float64(Float64(x - 7.0) * Float64(Float64(Float64(x - 6.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(Float64(x - 5.0) * Float64(x - 4.0)))))))) * 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 - 14.0) * (((x - 13.0) * (((x - 12.0) * (x - 11.0)) * ((x - 10.0) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))))) * (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[(x - 14.0), $MachinePrecision] * N[(N[(N[(x - 13.0), $MachinePrecision] * N[(N[(N[(x - 12.0), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $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%

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

3. Applied rewrites 97.8%

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

Alternative 10: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

MATLAB

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

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 11: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 12: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. 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

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*l* N/A

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

   5. associate-*l* N/A

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

   6. lower-*.f64 N/A

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

3. Applied rewrites 97.8%

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

Alternative 13: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

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

   2. *-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

3. Applied rewrites 97.7%

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

Alternative 14: 25.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 5.2:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot -19\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 5.2)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          (+ 17160.0 (* x (- (* x (+ 791.0 (* -46.0 x))) 6026.0)))
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
     -19.0)
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 5.2) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 <= 5.2d0) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * ((((17160.0d0 + (x * ((x * (791.0d0 + ((-46.0d0) * x))) - 6026.0d0))) * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) * (-19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 5.2) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 5.2:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	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)) * -19.0) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 5.2)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(Float64(17160.0 + Float64(x * Float64(Float64(x * Float64(791.0 + Float64(-46.0 * x))) - 6026.0))) * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) * -19.0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 5.2)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	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)) * -19.0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 5.2], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(N[(17160.0 + N[(x * N[(N[(x * N[(791.0 + N[(-46.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6026.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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] * -19.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.2000000000000002

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right)} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + \color{blue}{x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)}\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \color{blue}{\left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)}\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - \color{blue}{6026}\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      6. lower-*.f64 18.3%

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   8. Applied rewrites 18.3%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right)} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 5.2000000000000002 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 15.3%

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

Alternative 15: 23.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 8.8:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(\left(\left(\left(x - 12\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(380 + -39 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(36 + x \cdot \left(47 \cdot x - 72\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 8.8)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          (* (* (* (- x 12.0) (- x 13.0)) (- x 11.0)) (- x 10.0))
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (+ 380.0 (* -39.0 x))))
   (*
    (- x 18.0)
    (*
     (*
      (- 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)
              (*
               (+ 36.0 (* x (- (* 47.0 x) 72.0)))
               (* (- x 5.0) (- x 4.0))))))))))))
     (* (- x 20.0) (- x 19.0))))))

C

double code(double x) {
	double tmp;
	if (x <= 8.8) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((((((x - 12.0) * (x - 13.0)) * (x - 11.0)) * (x - 10.0)) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * (380.0 + (-39.0 * x)));
	} else {
		tmp = (x - 18.0) * (((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) * ((36.0 + (x * ((47.0 * x) - 72.0))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)));
	}
	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 <= 8.8d0) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((((((x - 12.0d0) * (x - 13.0d0)) * (x - 11.0d0)) * (x - 10.0d0)) * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * (380.0d0 + ((-39.0d0) * x)))
    else
        tmp = (x - 18.0d0) * (((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) * ((36.0d0 + (x * ((47.0d0 * x) - 72.0d0))) * ((x - 5.0d0) * (x - 4.0d0)))))))))))) * ((x - 20.0d0) * (x - 19.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 8.8) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((((((x - 12.0) * (x - 13.0)) * (x - 11.0)) * (x - 10.0)) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * (380.0 + (-39.0 * x)));
	} else {
		tmp = (x - 18.0) * (((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) * ((36.0 + (x * ((47.0 * x) - 72.0))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 8.8:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((((((x - 12.0) * (x - 13.0)) * (x - 11.0)) * (x - 10.0)) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * (380.0 + (-39.0 * x)))
	else:
		tmp = (x - 18.0) * (((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) * ((36.0 + (x * ((47.0 * x) - 72.0))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 8.8)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 12.0) * Float64(x - 13.0)) * Float64(x - 11.0)) * Float64(x - 10.0)) * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(380.0 + Float64(-39.0 * x))));
	else
		tmp = Float64(Float64(x - 18.0) * 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(Float64(x - 12.0) * Float64(x - 11.0)) * Float64(Float64(x - 10.0) * Float64(Float64(Float64(x - 9.0) * Float64(x - 8.0)) * Float64(Float64(x - 7.0) * Float64(Float64(36.0 + Float64(x * Float64(Float64(47.0 * x) - 72.0))) * Float64(Float64(x - 5.0) * Float64(x - 4.0)))))))))))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 8.8)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((((((x - 12.0) * (x - 13.0)) * (x - 11.0)) * (x - 10.0)) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * (380.0 + (-39.0 * x)));
	else
		tmp = (x - 18.0) * (((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) * ((36.0 + (x * ((47.0 * x) - 72.0))) * ((x - 5.0) * (x - 4.0)))))))))))) * ((x - 20.0) * (x - 19.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 8.8], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(x - 12.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(380.0 + N[(-39.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - 18.0), $MachinePrecision] * 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[(N[(x - 12.0), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 10.0), $MachinePrecision] * N[(N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(36.0 + N[(x * N[(N[(47.0 * x), $MachinePrecision] - 72.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.8000000000000007

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 19.5%

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

   8. Applied rewrites 19.5%

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

   if 8.8000000000000007 < x

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\color{blue}{\left(36 + x \cdot \left(47 \cdot x - 72\right)\right)} \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(36 + \color{blue}{x \cdot \left(47 \cdot x - 72\right)}\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(36 + x \cdot \color{blue}{\left(47 \cdot x - 72\right)}\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(36 + x \cdot \left(47 \cdot x - \color{blue}{72}\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      4. lower-*.f64 9.8%

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(36 + x \cdot \left(47 \cdot x - 72\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   6. Applied rewrites 9.8%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\color{blue}{\left(36 + x \cdot \left(47 \cdot x - 72\right)\right)} \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 21.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.8:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(791 \cdot x - 6026\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot -19\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.8)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          (+ 17160.0 (* x (- (* 791.0 x) 6026.0)))
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
     -19.0)
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 4.8) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 <= 4.8d0) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * ((((17160.0d0 + (x * ((791.0d0 * x) - 6026.0d0))) * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) * (-19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 4.8) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.8:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	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)) * -19.0) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.8)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(Float64(17160.0 + Float64(x * Float64(Float64(791.0 * x) - 6026.0))) * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) * -19.0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 4.8)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	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)) * -19.0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.8], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(N[(17160.0 + N[(x * N[(N[(791.0 * x), $MachinePrecision] - 6026.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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] * -19.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.7999999999999998

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{\left(17160 + x \cdot \left(791 \cdot x - 6026\right)\right)} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + \color{blue}{x \cdot \left(791 \cdot x - 6026\right)}\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \color{blue}{\left(791 \cdot x - 6026\right)}\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(791 \cdot x - \color{blue}{6026}\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

      4. lower-*.f64 18.7%

         \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(791 \cdot x - 6026\right)\right) \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   8. Applied rewrites 18.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{\left(17160 + x \cdot \left(791 \cdot x - 6026\right)\right)} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.7999999999999998 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 15.3%

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

Alternative 17: 19.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.25:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{elif}\;x \leq 13:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot -14\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.25)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (if (<= x 13.0)
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (* (* (* (- (* 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))
            -14.0)
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (- (* x (+ 13068.0 (* x (- (* 6769.0 x) 13132.0)))) 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)))))

C

double code(double x) {
	double tmp;
	if (x <= 4.25) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} else if (x <= 13.0) {
		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)) * -14.0) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((((((((((x * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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);
	}
	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 <= 4.25d0) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    else if (x <= 13.0d0) then
        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)) * (-14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((((((x * (13068.0d0 + (x * ((6769.0d0 * x) - 13132.0d0)))) - 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)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 4.25) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} else if (x <= 13.0) {
		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)) * -14.0) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = ((((((((((((((x * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.25:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	elif x <= 13.0:
		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)) * -14.0) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = ((((((((((((((x * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.25)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	elseif (x <= 13.0)
		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)) * -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(x * Float64(13068.0 + Float64(x * Float64(Float64(6769.0 * x) - 13132.0)))) - 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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 4.25)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	elseif (x <= 13.0)
		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)) * -14.0) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((((((x * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.25], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 13.0], 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] * -14.0), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x * N[(13068.0 + N[(x * N[(N[(6769.0 * x), $MachinePrecision] - 13132.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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]]]

Derivation

1. Split input into 3 regimes

2. if x < 4.25

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.25 < x < 13

   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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 13.9%

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

   if 13 < 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

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - \color{blue}{5040}\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-*.f64 11.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 11.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 19.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.3:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{elif}\;x \leq 12.6:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot -13\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.3)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (if (<= x 12.6)
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (* (* (* (- (* 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))
             -13.0)
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (- (* x (+ 13068.0 (* x (- (* 6769.0 x) 13132.0)))) 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)))))

C

double code(double x) {
	double tmp;
	if (x <= 4.3) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} else if (x <= 12.6) {
		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)) * -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 * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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);
	}
	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 <= 4.3d0) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    else if (x <= 12.6d0) then
        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)) * (-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 * (13068.0d0 + (x * ((6769.0d0 * x) - 13132.0d0)))) - 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)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 4.3) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} else if (x <= 12.6) {
		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)) * -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 * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.3:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	elif x <= 12.6:
		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)) * -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 * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.3)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	elseif (x <= 12.6)
		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)) * -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(x * Float64(13068.0 + Float64(x * Float64(Float64(6769.0 * x) - 13132.0)))) - 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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 4.3)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	elseif (x <= 12.6)
		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)) * -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 * (13068.0 + (x * ((6769.0 * x) - 13132.0)))) - 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);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.3], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12.6], 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] * -13.0), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x * N[(13068.0 + N[(x * N[(N[(6769.0 * x), $MachinePrecision] - 13132.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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]]]

Derivation

1. Split input into 3 regimes

2. if x < 4.2999999999999998

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.2999999999999998 < x < 12.6

   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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 13.5%

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

   if 12.6 < 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

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - \color{blue}{5040}\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-*.f64 11.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 11.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(x \cdot \left(13068 + x \cdot \left(6769 \cdot x - 13132\right)\right) - 5040\right)} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 19.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.46:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(x - 12\right) \cdot \left(\left(\left(\left(x - 11\right) \cdot \left(x - 10\right)\right) \cdot \left(72 \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right) \cdot \left(\left(x - 14\right) \cdot \left(x - 13\right)\right)\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot -19\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.46)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (- x 12.0)
          (*
           (*
            (* (- x 11.0) (- x 10.0))
            (*
             72.0
             (*
              (- x 7.0)
              (*
               (* (- x 6.0) (* (- x 3.0) (* (- x 2.0) (- x 1.0))))
               (* (- x 5.0) (- x 4.0))))))
           (* (- x 14.0) (- x 13.0))))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
     -19.0)
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 4.46) {
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (72.0 * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))) * ((x - 14.0) * (x - 13.0)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} 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)) * -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 <= 4.46d0) then
        tmp = (((((((x - 12.0d0) * ((((x - 11.0d0) * (x - 10.0d0)) * (72.0d0 * ((x - 7.0d0) * (((x - 6.0d0) * ((x - 3.0d0) * ((x - 2.0d0) * (x - 1.0d0)))) * ((x - 5.0d0) * (x - 4.0d0)))))) * ((x - 14.0d0) * (x - 13.0d0)))) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    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)) * (-19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 4.46) {
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (72.0 * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))) * ((x - 14.0) * (x - 13.0)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} 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)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.46:
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (72.0 * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))) * ((x - 14.0) * (x - 13.0)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	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)) * -19.0) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.46)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 12.0) * Float64(Float64(Float64(Float64(x - 11.0) * Float64(x - 10.0)) * Float64(72.0 * Float64(Float64(x - 7.0) * Float64(Float64(Float64(x - 6.0) * Float64(Float64(x - 3.0) * Float64(Float64(x - 2.0) * Float64(x - 1.0)))) * Float64(Float64(x - 5.0) * Float64(x - 4.0)))))) * Float64(Float64(x - 14.0) * Float64(x - 13.0)))) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) * -19.0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 4.46)
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (72.0 * ((x - 7.0) * (((x - 6.0) * ((x - 3.0) * ((x - 2.0) * (x - 1.0)))) * ((x - 5.0) * (x - 4.0)))))) * ((x - 14.0) * (x - 13.0)))) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	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)) * -19.0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.46], N[(N[(N[(N[(N[(N[(N[(N[(x - 12.0), $MachinePrecision] * N[(N[(N[(N[(x - 11.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(72.0 * N[(N[(x - 7.0), $MachinePrecision] * N[(N[(N[(x - 6.0), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 5.0), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 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] * -19.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.46

   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%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 17.6%

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

   if 4.46 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 15.3%

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

Alternative 20: 19.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Applied rewrites 97.7%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 19.0%

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

Alternative 21: 18.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.2:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot -19\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.2)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
     -19.0)
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 4.2) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) * (-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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -19.0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.2:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	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)) * -19.0) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.2)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) * -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	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)) * -19.0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.2], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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] * -19.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.2000000000000002

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.2000000000000002 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 15.3%

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

Alternative 22: 18.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.2:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot -18\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.2)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
      -18.0)
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 4.2) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) * (-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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -18.0) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.2:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	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)) * -18.0) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.2)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) * -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	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)) * -18.0) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.2], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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] * -18.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.2000000000000002

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.2000000000000002 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 15.1%

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

Alternative 23: 18.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.2:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot -17\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.2)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
       -17.0)
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 4.2) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) * (-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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	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)) * -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(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) * -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	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)) * -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[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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] * -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 x < 4.2000000000000002

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.2000000000000002 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 14.9%

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

Alternative 24: 18.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.2:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(11 \cdot x - 6\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot -16\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 4.2)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (* (* (- (* 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))
        -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) * (-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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} 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)) * -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	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)) * -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(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) * -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 - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	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)) * -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[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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] * -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 x < 4.2000000000000002

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 4.2000000000000002 < 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 14.8%

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

   4. Applied rewrites 14.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 14.7%

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

Alternative 25: 17.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 7.25:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(17160 \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(x - 12\right) \cdot \left(\left(\left(\left(x - 11\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)\right)\right)\right) \cdot \left(\left(x - 14\right) \cdot \left(x - 13\right)\right)\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 7.25)
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (*
       (- x 15.0)
       (*
        (*
         (*
          17160.0
          (*
           (*
            (* (- x 7.0) (* (- x 4.0) (- x 5.0)))
            (* (* (* (- x 3.0) (- x 6.0)) (- x 1.0)) (- x 2.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 16.0))))
     (* (- x 20.0) (- x 19.0))))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (- x 12.0)
          (*
           (*
            (* (- x 11.0) (- x 10.0))
            (*
             (* (- x 9.0) (- x 8.0))
             (* (- x 7.0) (+ 720.0 (* x (- (* 1624.0 x) 1764.0))))))
           (* (- x 14.0) (- x 13.0))))
         (- 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 <= 7.25) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} else {
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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 <= 7.25d0) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 15.0d0) * (((17160.0d0 * ((((x - 7.0d0) * ((x - 4.0d0) * (x - 5.0d0))) * ((((x - 3.0d0) * (x - 6.0d0)) * (x - 1.0d0)) * (x - 2.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 16.0d0)))) * ((x - 20.0d0) * (x - 19.0d0)))
    else
        tmp = (((((((x - 12.0d0) * ((((x - 11.0d0) * (x - 10.0d0)) * (((x - 9.0d0) * (x - 8.0d0)) * ((x - 7.0d0) * (720.0d0 + (x * ((1624.0d0 * x) - 1764.0d0)))))) * ((x - 14.0d0) * (x - 13.0d0)))) * (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 <= 7.25) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	} else {
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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 <= 7.25:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)))
	else:
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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 <= 7.25)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 15.0) * Float64(Float64(Float64(17160.0 * Float64(Float64(Float64(Float64(x - 7.0) * Float64(Float64(x - 4.0) * Float64(x - 5.0))) * Float64(Float64(Float64(Float64(x - 3.0) * Float64(x - 6.0)) * Float64(x - 1.0)) * Float64(x - 2.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 16.0)))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 12.0) * Float64(Float64(Float64(Float64(x - 11.0) * Float64(x - 10.0)) * Float64(Float64(Float64(x - 9.0) * Float64(x - 8.0)) * Float64(Float64(x - 7.0) * Float64(720.0 + Float64(x * Float64(Float64(1624.0 * x) - 1764.0)))))) * Float64(Float64(x - 14.0) * Float64(x - 13.0)))) * 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 <= 7.25)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 15.0) * (((17160.0 * ((((x - 7.0) * ((x - 4.0) * (x - 5.0))) * ((((x - 3.0) * (x - 6.0)) * (x - 1.0)) * (x - 2.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 16.0)))) * ((x - 20.0) * (x - 19.0)));
	else
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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, 7.25], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * N[(N[(N[(17160.0 * N[(N[(N[(N[(x - 7.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 3.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 8.0), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(x - 12.0), $MachinePrecision] * N[(N[(N[(N[(x - 11.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(720.0 + N[(x * N[(N[(1624.0 * x), $MachinePrecision] - 1764.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.25

   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%

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 15.7%

      \[\leadsto \left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(\left(\color{blue}{17160} \cdot \left(\left(\left(\left(x - 7\right) \cdot \left(\left(x - 4\right) \cdot \left(x - 5\right)\right)\right) \cdot \left(\left(\left(\left(x - 3\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 2\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 16\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right) \]

   if 7.25 < x

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 9.8%

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

   6. Applied rewrites 9.8%

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

Alternative 26: 15.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -6000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{7} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -6000000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (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))
    -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))
       (- 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)) <= -6000000000000.0) {
		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)) * -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)) * (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)) <= (-6000000000000.0d0)) 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)) * (-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)) * (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)) <= -6000000000000.0) {
		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)) * -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)) * (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)) <= -6000000000000.0:
		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)) * -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)) * (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)) <= -6000000000000.0)
		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)) * -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)) * 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)) <= -6000000000000.0)
		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)) * -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)) * (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], -6000000000000.0], 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] * -20.0), $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] * 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))) < -6e12

   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 12.0%

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

   4. Applied rewrites 12.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 11.7%

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

   if -6e12 < (*.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%

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

Alternative 27: 15.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 2200000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(274 \cdot x - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      2200000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (* (- (* 274.0 x) 120.0) (- x 6.0)) (- x 7.0)) (- x 8.0))
               (- x 9.0))
              (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- 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)) <= 2200000000000.0) {
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (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)) <= 2200000000000.0d0) then
        tmp = ((((((((((((((((274.0d0 * x) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 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)) <= 2200000000000.0) {
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (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)) <= 2200000000000.0:
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (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)) <= 2200000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(274.0 * x) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(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)) <= 2200000000000.0)
		tmp = ((((((((((((((((274.0 * x) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (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], 2200000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(274.0 * x), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(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))) < 2.2e12

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 12.8%

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

   4. Applied rewrites 12.8%

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

   if 2.2e12 < (*.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 8.1%

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

   4. Applied rewrites 8.1%

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

Alternative 28: 15.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -1000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{7} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(x - 12\right) \cdot \left(\left(\left(\left(x - 11\right) \cdot \left(x - 10\right)\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(720 + x \cdot \left(1624 \cdot x - 1764\right)\right)\right)\right)\right) \cdot \left(\left(x - 14\right) \cdot \left(x - 13\right)\right)\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (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))
    -20.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (- x 12.0)
          (*
           (*
            (* (- x 11.0) (- x 10.0))
            (*
             (* (- x 9.0) (- x 8.0))
             (* (- x 7.0) (+ 720.0 (* x (- (* 1624.0 x) 1764.0))))))
           (* (- x 14.0) (- x 13.0))))
         (- 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 = ((((((((((((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)) * -20.0;
	} else {
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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 = (((((((((((((x ** 7.0d0) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (-20.0d0)
    else
        tmp = (((((((x - 12.0d0) * ((((x - 11.0d0) * (x - 10.0d0)) * (((x - 9.0d0) * (x - 8.0d0)) * ((x - 7.0d0) * (720.0d0 + (x * ((1624.0d0 * x) - 1764.0d0)))))) * ((x - 14.0d0) * (x - 13.0d0)))) * (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 = ((((((((((((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)) * -20.0;
	} else {
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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 = ((((((((((((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)) * -20.0
	else:
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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((x ^ 7.0) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * -20.0);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 12.0) * Float64(Float64(Float64(Float64(x - 11.0) * Float64(x - 10.0)) * Float64(Float64(Float64(x - 9.0) * Float64(x - 8.0)) * Float64(Float64(x - 7.0) * Float64(720.0 + Float64(x * Float64(Float64(1624.0 * x) - 1764.0)))))) * Float64(Float64(x - 14.0) * Float64(x - 13.0)))) * 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 = (((((((((((((x ^ 7.0) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	else
		tmp = (((((((x - 12.0) * ((((x - 11.0) * (x - 10.0)) * (((x - 9.0) * (x - 8.0)) * ((x - 7.0) * (720.0 + (x * ((1624.0 * x) - 1764.0)))))) * ((x - 14.0) * (x - 13.0)))) * (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[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] * -20.0), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(x - 12.0), $MachinePrecision] * N[(N[(N[(N[(x - 11.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 9.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 7.0), $MachinePrecision] * N[(720.0 + N[(x * N[(N[(1624.0 * x), $MachinePrecision] - 1764.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -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 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 12.0%

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

   4. Applied rewrites 12.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 11.7%

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

   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%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 9.8%

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

   6. Applied rewrites 9.8%

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

Alternative 29: 15.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -920000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{7} \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -920000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (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))
    -20.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (* 720.0 (- x 7.0)) (- x 8.0)) (- x 9.0)) (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- 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)) <= -920000000000.0) {
		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)) * -20.0;
	} else {
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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)) <= (-920000000000.0d0)) 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)) * (-20.0d0)
    else
        tmp = (((((((((((((720.0d0 * (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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -920000000000.0) {
		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)) * -20.0;
	} else {
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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)) <= -920000000000.0:
		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)) * -20.0
	else:
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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)) <= -920000000000.0)
		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)) * -20.0);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(720.0 * 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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -920000000000.0)
		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)) * -20.0;
	else
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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], -920000000000.0], 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] * -20.0), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(720.0 * 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 (*.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))) < -9.2e11

   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 12.0%

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

   4. Applied rewrites 12.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 11.7%

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

   if -9.2e11 < (*.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

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

   4. Applied rewrites 9.3%

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

Alternative 30: 14.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -920000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{9} \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -920000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (* (pow x 9.0) (- x 10.0)) (- x 11.0)) (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (* 720.0 (- x 7.0)) (- x 8.0)) (- x 9.0)) (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- 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)) <= -920000000000.0) {
		tmp = ((((((((((pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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)) <= (-920000000000.0d0)) then
        tmp = (((((((((((x ** 9.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((720.0d0 * (x - 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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -920000000000.0) {
		tmp = ((((((((((Math.pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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)) <= -920000000000.0:
		tmp = ((((((((((math.pow(x, 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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)) <= -920000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 9.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(720.0 * 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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -920000000000.0)
		tmp = (((((((((((x ^ 9.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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], -920000000000.0], 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[(N[(N[(N[(720.0 * 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 (*.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))) < -9.2e11

   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 10.7%

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

   4. Applied rewrites 10.7%

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

   if -9.2e11 < (*.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

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

   4. Applied rewrites 9.3%

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

Alternative 31: 14.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -1000000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \left(3731 + -91 \cdot x\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(720 \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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)
   (*
    (*
     (*
      (*
       (*
        (* (* (* (pow x 11.0) (+ 3731.0 (* -91.0 x))) (- x 14.0)) (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (* (* 720.0 (- x 7.0)) (- x 8.0)) (- x 9.0)) (- x 10.0))
             (- x 11.0))
            (- x 12.0))
           (- 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 = (((((((pow(x, 11.0) * (3731.0 + (-91.0 * x))) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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 = ((((((((x ** 11.0d0) * (3731.0d0 + ((-91.0d0) * x))) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((((((((((((720.0d0 * (x - 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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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 = (((((((Math.pow(x, 11.0) * (3731.0 + (-91.0 * x))) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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 = (((((((math.pow(x, 11.0) * (3731.0 + (-91.0 * x))) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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((x ^ 11.0) * Float64(3731.0 + Float64(-91.0 * x))) * 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(720.0 * 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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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 = ((((((((x ^ 11.0) * (3731.0 + (-91.0 * x))) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((((((((((((720.0 * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (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[Power[x, 11.0], $MachinePrecision] * N[(3731.0 + N[(-91.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(720.0 * 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 (*.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 inf

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \color{blue}{\left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \frac{1}{x}\right)}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\color{blue}{\left(1 + \frac{3731}{{x}^{2}}\right)} - 91 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - \color{blue}{91 \cdot \frac{1}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - \color{blue}{91} \cdot \frac{1}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      6. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \frac{1}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \color{blue}{\frac{1}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      8. lower-/.f64 9.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \frac{1}{\color{blue}{x}}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 9.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{\left({x}^{13} \cdot \left(\left(1 + \frac{3731}{{x}^{2}}\right) - 91 \cdot \frac{1}{x}\right)\right)} \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \color{blue}{\left(3731 + -91 \cdot x\right)}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \left(3731 + \color{blue}{-91 \cdot x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-pow.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \left(3731 + \color{blue}{-91} \cdot x\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \left(3731 + -91 \cdot \color{blue}{x}\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 9.3%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \left(3731 + -91 \cdot x\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   7. Applied rewrites 9.3%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left({x}^{11} \cdot \color{blue}{\left(3731 + -91 \cdot x\right)}\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   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 0

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

   4. Applied rewrites 9.3%

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

Alternative 32: 14.3% 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 11.4%

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

   4. Applied rewrites 11.4%

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

   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 8.1%

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

   4. Applied rewrites 8.1%

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

Alternative 33: 14.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 1026576.0 x) 362880.0) (- x 10.0)) (- x 11.0))
            (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (* (pow x 10.0) (- x 11.0)) (- x 12.0)) (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 40000000000.0d0) then
        tmp = ((((((((((((1026576.0d0 * x) - 362880.0d0) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = ((((((((((x ** 10.0d0) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((((((((Math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0:
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((((((((math.pow(x, 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 40000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1026576.0 * x) - 362880.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64((x ^ 10.0) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0)
		tmp = ((((((((((((1026576.0 * x) - 362880.0) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = ((((((((((x ^ 10.0) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 40000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1026576.0 * x), $MachinePrecision] - 362880.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[Power[x, 10.0], $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   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 10.7%

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

   4. Applied rewrites 10.7%

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

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

   1. Initial program 97.8%

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

   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 8.1%

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

   4. Applied rewrites 8.1%

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

Alternative 34: 13.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(40320 \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 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))
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (* (* 40320.0 (- x 9.0)) (- x 10.0)) (- x 11.0)) (- x 12.0))
           (- x 13.0))
          (- x 14.0))
         (- x 15.0))
        (- x 16.0))
       (- x 17.0))
      (- x 18.0))
     (- x 19.0))
    (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((((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 = (((((((((((40320.0 * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 40000000000.0d0) then
        tmp = ((((((((((((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 = (((((((((((40320.0d0 * (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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((((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 = (((((((((((40320.0 * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0:
		tmp = ((((((((((((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 = (((((((((((40320.0 * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 40000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(1026576.0 * x) - 362880.0) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(40320.0 * 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 - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0)
		tmp = ((((((((((((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 = (((((((((((40320.0 * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 40000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(1026576.0 * x), $MachinePrecision] - 362880.0), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(40320.0 * 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 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < 4e10

   1. Initial program 97.8%

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

   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 10.7%

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

   4. Applied rewrites 10.7%

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

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{40320} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 8.2%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{40320} \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 35: 13.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot {x}^{12}\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (* (* (- (* 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))
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (* (- x 16.0) (* (- x 15.0) (* (- x 14.0) (* (- x 13.0) (pow x 12.0))))))
     (* (- x 20.0) (- x 19.0))))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * pow(x, 12.0)))))) * ((x - 20.0) * (x - 19.0)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 40000000000.0d0) then
        tmp = ((((((((((((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 - 18.0d0) * (((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * (x ** 12.0d0)))))) * ((x - 20.0d0) * (x - 19.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * Math.pow(x, 12.0)))))) * ((x - 20.0) * (x - 19.0)));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0:
		tmp = ((((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * math.pow(x, 12.0)))))) * ((x - 20.0) * (x - 19.0)))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 40000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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(x - 18.0) * 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) * (x ^ 12.0)))))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0)
		tmp = ((((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * (x ^ 12.0)))))) * ((x - 20.0) * (x - 19.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 40000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(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[(x - 18.0), $MachinePrecision] * 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[Power[x, 12.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.8%

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

   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 10.7%

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

   4. Applied rewrites 10.7%

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

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

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.4%

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

   6. Applied rewrites 7.4%

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

Alternative 36: 13.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot {x}^{12}\right)\right)\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      40000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (- (* 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))
   (*
    (- x 18.0)
    (*
     (*
      (- x 17.0)
      (* (- x 16.0) (* (- x 15.0) (* (- x 14.0) (* (- x 13.0) (pow x 12.0))))))
     (* (- x 20.0) (- x 19.0))))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * pow(x, 12.0)))))) * ((x - 20.0) * (x - 19.0)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= 40000000000.0d0) then
        tmp = ((((((((((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 - 18.0d0) * (((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * (x ** 12.0d0)))))) * ((x - 20.0d0) * (x - 19.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0) {
		tmp = ((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * Math.pow(x, 12.0)))))) * ((x - 20.0) * (x - 19.0)));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0:
		tmp = ((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * math.pow(x, 12.0)))))) * ((x - 20.0) * (x - 19.0)))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= 40000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(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(x - 18.0) * 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) * (x ^ 12.0)))))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= 40000000000.0)
		tmp = ((((((((((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 - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * ((x - 14.0) * ((x - 13.0) * (x ^ 12.0)))))) * ((x - 20.0) * (x - 19.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], 40000000000.0], N[(N[(N[(N[(N[(N[(N[(N[(N[(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[(x - 18.0), $MachinePrecision] * 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[Power[x, 12.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.8%

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

   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 10.1%

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

   4. Applied rewrites 10.1%

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

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

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.4%

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

   6. Applied rewrites 7.4%

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

Alternative 37: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -5000000000.0)
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (* (- (* 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)) <= -5000000000.0) {
		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)) <= (-5000000000.0d0)) 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)) <= -5000000000.0) {
		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)) <= -5000000000.0:
		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)) <= -5000000000.0)
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   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 10.1%

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

   4. Applied rewrites 10.1%

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

   if -5e9 < (*.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 7.8%

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

Alternative 38: 13.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 40000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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

   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 10.1%

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

   4. Applied rewrites 10.1%

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

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

   1. Initial program 97.8%

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

   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 7.4%

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

Alternative 39: 13.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(479001600 \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -5000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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)) <= -5000000000.0) {
		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)) <= (-5000000000.0d0)) 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)) <= -5000000000.0) {
		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)) <= -5000000000.0:
		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)) <= -5000000000.0)
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   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 9.5%

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

   4. Applied rewrites 9.5%

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

   if -5e9 < (*.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 7.4%

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

Alternative 40: 13.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(19802759040 \cdot x - 6227020800\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot 87178291200\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \end{array} \]

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))
      -5000000000.0)
   (*
    (*
     (*
      (*
       (*
        (* (* (- (* 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))
   (*
    (- x 18.0)
    (*
     (* (- x 17.0) (* (- x 16.0) (* (- x 15.0) 87178291200.0)))
     (* (- x 20.0) (- x 19.0))))))

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)) <= -5000000000.0) {
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * ((x - 20.0) * (x - 19.0)));
	}
	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)) <= (-5000000000.0d0)) then
        tmp = ((((((((19802759040.0d0 * x) - 6227020800.0d0) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * 87178291200.0d0))) * ((x - 20.0d0) * (x - 19.0d0)))
    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)) <= -5000000000.0) {
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * ((x - 20.0) * (x - 19.0)));
	}
	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)) <= -5000000000.0:
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * ((x - 20.0) * (x - 19.0)))
	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)) <= -5000000000.0)
		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(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * 87178291200.0))) * Float64(Float64(x - 20.0) * Float64(x - 19.0))));
	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)) <= -5000000000.0)
		tmp = ((((((((19802759040.0 * x) - 6227020800.0) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * ((x - 20.0) * (x - 19.0)));
	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], -5000000000.0], 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[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * 87178291200.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]), $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))) < -5e9

   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 9.5%

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

   4. Applied rewrites 9.5%

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

   if -5e9 < (*.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%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 6.9%

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

Alternative 41: 13.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(x - 20\right) \cdot \left(x - 19\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(4339163001600 \cdot x - 1307674368000\right)\right)\right) \cdot t\_0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot 87178291200\right)\right)\right) \cdot t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (- x 20.0) (- x 19.0))))
   (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))
        -5000000000.0)
     (*
      (- x 18.0)
      (*
       (* (- x 17.0) (* (- x 16.0) (- (* 4339163001600.0 x) 1307674368000.0)))
       t_0))
     (*
      (- x 18.0)
      (* (* (- x 17.0) (* (- x 16.0) (* (- x 15.0) 87178291200.0))) t_0)))))

C

double code(double x) {
	double t_0 = (x - 20.0) * (x - 19.0);
	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)) <= -5000000000.0) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * t_0);
	} else {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * t_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) :: t_0
    real(8) :: tmp
    t_0 = (x - 20.0d0) * (x - 19.0d0)
    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)) <= (-5000000000.0d0)) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 16.0d0) * ((4339163001600.0d0 * x) - 1307674368000.0d0))) * t_0)
    else
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * 87178291200.0d0))) * t_0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x - 20.0) * (x - 19.0);
	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)) <= -5000000000.0) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * t_0);
	} else {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * t_0);
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x - 20.0) * (x - 19.0)
	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)) <= -5000000000.0:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * t_0)
	else:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * t_0)
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x - 20.0) * Float64(x - 19.0))
	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)) <= -5000000000.0)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(4339163001600.0 * x) - 1307674368000.0))) * t_0));
	else
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * 87178291200.0))) * t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x - 20.0) * (x - 19.0);
	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)) <= -5000000000.0)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * t_0);
	else
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))) * t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision]}, 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], -5000000000.0], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(4339163001600.0 * x), $MachinePrecision] - 1307674368000.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * 87178291200.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$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))) < -5e9

   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%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.9%

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

   6. Applied rewrites 8.9%

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

   if -5e9 < (*.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%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 6.9%

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

Alternative 42: 12.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(x - 18\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(4339163001600 \cdot x - 1307674368000\right)\right)\right) \cdot \left(\left(x - 20\right) \cdot \left(x - 19\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

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))
      -5000000000.0)
   (*
    (- x 18.0)
    (*
     (* (- x 17.0) (* (- x 16.0) (- (* 4339163001600.0 x) 1307674368000.0)))
     (* (- 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)) <= -5000000000.0) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * ((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)) <= (-5000000000.0d0)) then
        tmp = (x - 18.0d0) * (((x - 17.0d0) * ((x - 16.0d0) * ((4339163001600.0d0 * x) - 1307674368000.0d0))) * ((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)) <= -5000000000.0) {
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * ((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)) <= -5000000000.0:
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * ((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)) <= -5000000000.0)
		tmp = Float64(Float64(x - 18.0) * Float64(Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(4339163001600.0 * x) - 1307674368000.0))) * 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)) <= -5000000000.0)
		tmp = (x - 18.0) * (((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))) * ((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], -5000000000.0], N[(N[(x - 18.0), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(4339163001600.0 * x), $MachinePrecision] - 1307674368000.0), $MachinePrecision]), $MachinePrecision]), $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))) < -5e9

   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%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.9%

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

   6. Applied rewrites 8.9%

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

   if -5e9 < (*.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 5.8%

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

   4. Applied rewrites 5.8%

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

Alternative 43: 12.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<=
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (* (- x 1.0) (- x 2.0)) (- x 3.0)) (- x 4.0))
                      (- x 5.0))
                     (- x 6.0))
                    (- x 7.0))
                   (- x 8.0))
                  (- x 9.0))
                 (- x 10.0))
                (- x 11.0))
               (- x 12.0))
              (- x 13.0))
             (- x 14.0))
            (- x 15.0))
           (- x 16.0))
          (- x 17.0))
         (- x 18.0))
        (- x 19.0))
       (- x 20.0))
      -5000000000.0)
   (*
    (*
     (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
     (- x 19.0))
    (- x 20.0))
   (pow x 20.0)))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -5000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = pow(x, 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-5000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = x ** 20.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -5000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = Math.pow(x, 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -5000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = math.pow(x, 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -5000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = x ^ 20.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -5000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = x ^ 20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -5000000000.0], N[(N[(N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[Power[x, 20.0], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -5e9

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \left(\left(\color{blue}{\left(1223405590579200 \cdot x - 355687428096000\right)} \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.5%

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

   4. Applied rewrites 8.5%

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

   if -5e9 < (*.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 5.8%

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

   4. Applied rewrites 5.8%

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

Alternative 44: 12.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;{x}^{20}\\ \end{array} \]

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))
      -5000000000.0)
   (* (- (* 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)) <= -5000000000.0) {
		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)) <= (-5000000000.0d0)) 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)) <= -5000000000.0) {
		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)) <= -5000000000.0:
		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)) <= -5000000000.0)
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.1%

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

   4. Applied rewrites 8.1%

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

   if -5e9 < (*.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 5.8%

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

   4. Applied rewrites 5.8%

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

Alternative 45: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -5000000000.0)
   (* (- (* 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)) <= -5000000000.0) {
		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)) <= (-5000000000.0d0)) 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)) <= -5000000000.0) {
		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)) <= -5000000000.0:
		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)) <= -5000000000.0)
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.1%

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

   4. Applied rewrites 8.1%

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

   if -5e9 < (*.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

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -5000000000.0)
   (* (- (* 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)) <= -5000000000.0) {
		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)) <= (-5000000000.0d0)) 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)) <= -5000000000.0) {
		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)) <= -5000000000.0:
		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)) <= -5000000000.0)
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(431565146817638400 \cdot x - 121645100408832000\right)} \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 8.1%

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

   4. Applied rewrites 8.1%

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

   if -5e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.7%

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

Alternative 47: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
      -5000000000.0)
   (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)) <= -5000000000.0) {
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   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%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.0%

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

   6. Applied rewrites 8.0%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   7. 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 8.0%

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

   8. Applied rewrites 8.0%

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

   if -5e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.7%

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

Alternative 48: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

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))
      -5000000000.0)
   (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)) <= -5000000000.0) {
		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)) <= -5000000000.0)
		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], -5000000000.0], 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))) < -5e9

   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%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.0%

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

   6. Applied rewrites 8.0%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   7. 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 8.0%

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

   8. Applied rewrites 8.0%

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

   if -5e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.7%

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

Alternative 49: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -5000000000:\\ \;\;\;\;-8.7529480367616 \cdot 10^{+18} \cdot x\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

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))
      -5000000000.0)
   (* -8.7529480367616e+18 x)
   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)) <= -5000000000.0) {
		tmp = -8.7529480367616e+18 * x;
	} else {
		tmp = 2.43290200817664e+18;
	}
	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)) <= (-5000000000.0d0)) then
        tmp = (-8.7529480367616d+18) * x
    else
        tmp = 2.43290200817664d+18
    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)) <= -5000000000.0) {
		tmp = -8.7529480367616e+18 * x;
	} else {
		tmp = 2.43290200817664e+18;
	}
	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)) <= -5000000000.0:
		tmp = -8.7529480367616e+18 * x
	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)) <= -5000000000.0)
		tmp = Float64(-8.7529480367616e+18 * x);
	else
		tmp = 2.43290200817664e+18;
	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)) <= -5000000000.0)
		tmp = -8.7529480367616e+18 * x;
	else
		tmp = 2.43290200817664e+18;
	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], -5000000000.0], N[(-8.7529480367616e+18 * x), $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))) < -5e9

   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%

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

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2432902008176640000 + -8752948036761600000 \cdot x} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2432902008176640000 + \color{blue}{-8752948036761600000 \cdot x} \]

      2. lower-*.f64 8.0%

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

   6. Applied rewrites 8.0%

      \[\leadsto \color{blue}{2.43290200817664 \cdot 10^{+18} + -8.7529480367616 \cdot 10^{+18} \cdot x} \]
   7. 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 8.0%

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

   8. Applied rewrites 8.0%

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

   9. Taylor expanded in x around inf

      \[\leadsto -8752948036761600000 \cdot \color{blue}{x} \]
   10. Step-by-step derivation

       1. lower-*.f64 8.0%

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

   11. Applied rewrites 8.0%

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

   if -5e9 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 5.7%

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

Alternative 50: 5.7% accurate, 110.0× speedup

Math

\[2.43290200817664 \cdot 10^{+18} \]

FPCore

(FPCore (x) :precision binary64 2.43290200817664e+18)

C

double code(double x) {
	return 2.43290200817664e+18;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = 2.43290200817664d+18
end function

Java

public static double code(double x) {
	return 2.43290200817664e+18;
}

Python

def code(x):
	return 2.43290200817664e+18

Julia

function code(x)
	return 2.43290200817664e+18
end

MATLAB

function tmp = code(x)
	tmp = 2.43290200817664e+18;
end

Wolfram

code[x_] := 2.43290200817664e+18

Derivation

1. Initial program 97.8%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 5.7%

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

Reproduce

herbie shell --seed 2025205 
(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)))