(x - 1) to (x - 20)

Percentage Accurate: 97.8% → 98.0%

Time: 20.2s

Alternatives: 43

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

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

FPCore

(FPCore (x)
  :precision binary64
  (*
 (*
  (*
   (- 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 4.0) (* (- x 2.0) (- x 3.0))) (- x 1.0))
         (* (- x 5.0) (* (- x 6.0) (- x 7.0))))))))))
  (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0))))
 (- x 20.0)))

C

double code(double x) {
	return (((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 - 4.0) * ((x - 2.0) * (x - 3.0))) * (x - 1.0)) * ((x - 5.0) * ((x - 6.0) * (x - 7.0)))))))))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
}

Julia

function code(x)
	return Float64(Float64(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(Float64(Float64(x - 4.0) * Float64(Float64(x - 2.0) * Float64(x - 3.0))) * Float64(x - 1.0)) * Float64(Float64(x - 5.0) * Float64(Float64(x - 6.0) * Float64(x - 7.0)))))))))) * Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * Float64(x - 20.0))
end

Wolfram

code[x_] := N[(N[(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[(N[(N[(x - 4.0), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 5.0), $MachinePrecision] * N[(N[(x - 6.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

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

7. Applied rewrites 98.0%

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

9. Applied rewrites 98.0%

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

Alternative 2: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

function code(x)
	return Float64(Float64(Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * Float64(fma(x, Float64(Float64(x - 11.0) + -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(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * Float64(x - 20.0))
end

Wolfram

code[x_] := N[(N[(N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(N[(x * N[(N[(x - 11.0), $MachinePrecision] + -12.0), $MachinePrecision] + 132.0), $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[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

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

7. Applied rewrites 98.0%

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

   1. lift-fma.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. associate-+r+ N/A

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

   4. *-commutative N/A

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

   5. distribute-rgt-out N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-+.f64 98.0%

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

9. Applied rewrites 98.0%

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

Alternative 3: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_] := N[(N[(N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * N[(N[(N[(N[(x - 10.0), $MachinePrecision] * N[(x * N[(N[(x - 11.0), $MachinePrecision] + -12.0), $MachinePrecision] + 132.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 7.0), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

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

7. Applied rewrites 98.0%

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

9. Applied rewrites 97.9%

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

Alternative 4: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

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

7. Applied rewrites 98.0%

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

9. Applied rewrites 98.0%

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

Alternative 5: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval 98.0%

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

7. Applied rewrites 98.0%

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

9. Applied rewrites 98.0%

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

Alternative 6: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x) {
	return ((x - 20.0) * (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)))))))))))));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = ((x - 20.0d0) * (x - 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)))))))))))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x) {
	return ((x - 17.0) * (((((((((x - 12.0) * (x - 13.0)) * (x - 11.0)) * (x - 10.0)) * ((((x - 5.0) * ((x - 4.0) * (x - 7.0))) * ((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 6.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * ((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 - 17.0d0) * (((((((((x - 12.0d0) * (x - 13.0d0)) * (x - 11.0d0)) * (x - 10.0d0)) * ((((x - 5.0d0) * ((x - 4.0d0) * (x - 7.0d0))) * ((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 6.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * ((x - 18.0d0) * (x - 19.0d0)))) * (x - 20.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(N[(N[(x - 17.0), $MachinePrecision] * N[(N[(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 - 5.0), $MachinePrecision] * N[(N[(x - 4.0), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $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 - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $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%

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

5. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 97.8%

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

7. Applied rewrites 97.8%

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

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x) {
	return (x - 17.0) * (((((x - 16.0) * (((((((x - 12.0) * (x - 13.0)) * (x - 11.0)) * (x - 10.0)) * ((((x - 7.0) * (((x - 4.0) * (x - 5.0)) * (x - 6.0))) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (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 - 17.0d0) * (((((x - 16.0d0) * (((((((x - 12.0d0) * (x - 13.0d0)) * (x - 11.0d0)) * (x - 10.0d0)) * ((((x - 7.0d0) * (((x - 4.0d0) * (x - 5.0d0)) * (x - 6.0d0))) * (((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 15.0d0))) * (x - 19.0d0)) * (x - 18.0d0)) * (x - 20.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(N[(x - 17.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 16.0), $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[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $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 - 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $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%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift--.f64 N/A

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

   4. sub-flip N/A

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

   5. distribute-lft-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. metadata-eval 97.9%

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

5. Applied rewrites 97.9%

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

7. Applied rewrites 97.8%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. associate-*l* N/A

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

   8. lower-*.f64 N/A

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

   9. lower-*.f64 97.8%

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lift-*.f64 97.8%

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

9. Applied rewrites 97.8%

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

Alternative 9: 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 10: 97.8% accurate, 1.0× speedup

Math

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

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 13.0) (- x 12.0))))
       (- x 14.0))
      (- x 15.0))
     (- x 16.0))
    (- x 17.0))
   (- x 18.0))
  (- x 19.0))
 (- x 20.0)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    code = ((((((((((x - 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 - 13.0d0) * (x - 12.0d0)))) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(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[(N[(x - 13.0), $MachinePrecision] * N[(x - 12.0), $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] * 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%

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

Alternative 11: 97.8% accurate, 1.0× speedup

Math

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

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 97.8%

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

Alternative 12: 28.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 8.6:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 8.6)
  (*
   (*
    (*
     (- 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))))))))))
    (+ 93024.0 (* x (- (* x (+ 1835.0 (* -70.0 x))) 21350.0))))
   (- x 20.0))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (- (* x (+ 274.0 (* x (- (* 85.0 x) 225.0)))) 120.0)
                 (- x 6.0))
                (- x 7.0))
               (- x 8.0))
              (- x 9.0))
             (- x 10.0))
            (- x 11.0))
           (- x 12.0))
          (- x 13.0))
         (- x 14.0))
        (- x 15.0))
       (- x 16.0))
      (- x 17.0))
     (- x 18.0))
    (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 8.6) {
		tmp = (((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)))))))))) * (93024.0 + (x * ((x * (1835.0 + (-70.0 * x))) - 21350.0)))) * (x - 20.0);
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 8.6d0) then
        tmp = (((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)))))))))) * (93024.0d0 + (x * ((x * (1835.0d0 + ((-70.0d0) * x))) - 21350.0d0)))) * (x - 20.0d0)
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 8.6) {
		tmp = (((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)))))))))) * (93024.0 + (x * ((x * (1835.0 + (-70.0 * x))) - 21350.0)))) * (x - 20.0);
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 8.6:
		tmp = (((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)))))))))) * (93024.0 + (x * ((x * (1835.0 + (-70.0 * x))) - 21350.0)))) * (x - 20.0)
	else:
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 8.6)
		tmp = Float64(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(93024.0 + Float64(x * Float64(Float64(x * Float64(1835.0 + Float64(-70.0 * x))) - 21350.0)))) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 8.6)
		tmp = (((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)))))))))) * (93024.0 + (x * ((x * (1835.0 + (-70.0 * x))) - 21350.0)))) * (x - 20.0);
	else
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 8.6], N[(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[(93024.0 + N[(x * N[(N[(x * N[(1835.0 + N[(-70.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 21350.0), $MachinePrecision]), $MachinePrecision]), $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[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.5999999999999996

   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%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)\right)}\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + \color{blue}{x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)}\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \color{blue}{\left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)}\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - \color{blue}{21350}\right)\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)\right)\right) \cdot \left(x - 20\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)\right)\right) \cdot \left(x - 20\right) \]

      6. lower-*.f64 23.7%

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 23.7%

      \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(93024 + x \cdot \left(x \cdot \left(1835 + -70 \cdot x\right) - 21350\right)\right)}\right) \cdot \left(x - 20\right) \]

   if 8.5999999999999996 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 13.7%

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

   4. Applied rewrites 13.7%

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

Alternative 13: 24.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 4.5:\\ \;\;\;\;\left(x - 17\right) \cdot \left(\left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(x \cdot \left(791 + -46 \cdot x\right) - 6026\right)\right) \cdot \left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-20 \cdot \left(x - 19\right)\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 4.5)
  (*
   (- x 17.0)
   (*
    (*
     (*
      (*
       (- x 16.0)
       (*
        (*
         (*
          (+ 17160.0 (* x (- (* x (+ 791.0 (* -46.0 x))) 6026.0)))
          (*
           (*
            (* (* (* (- x 4.0) (- x 5.0)) (- x 7.0)) (- x 6.0))
            (* (* (- x 1.0) (- x 2.0)) (- x 3.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 15.0)))
      (- x 19.0))
     (- x 18.0))
    (- x 20.0)))
  (*
   (* -20.0 (- 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))))))))))))))))

C

double code(double x) {
	double tmp;
	if (x <= 4.5) {
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	} else {
		tmp = (-20.0 * (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)))))))))))));
	}
	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 <= 4.5d0) then
        tmp = (x - 17.0d0) * (((((x - 16.0d0) * ((((17160.0d0 + (x * ((x * (791.0d0 + ((-46.0d0) * x))) - 6026.0d0))) * ((((((x - 4.0d0) * (x - 5.0d0)) * (x - 7.0d0)) * (x - 6.0d0)) * (((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 15.0d0))) * (x - 19.0d0)) * (x - 18.0d0)) * (x - 20.0d0))
    else
        tmp = ((-20.0d0) * (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)))))))))))))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 4.5) {
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	} else {
		tmp = (-20.0 * (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)))))))))))));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 4.5:
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0))
	else:
		tmp = (-20.0 * (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)))))))))))))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 4.5)
		tmp = Float64(Float64(x - 17.0) * Float64(Float64(Float64(Float64(Float64(x - 16.0) * Float64(Float64(Float64(Float64(17160.0 + Float64(x * Float64(Float64(x * Float64(791.0 + Float64(-46.0 * x))) - 6026.0))) * Float64(Float64(Float64(Float64(Float64(Float64(x - 4.0) * Float64(x - 5.0)) * Float64(x - 7.0)) * Float64(x - 6.0)) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 15.0))) * Float64(x - 19.0)) * Float64(x - 18.0)) * Float64(x - 20.0)));
	else
		tmp = Float64(Float64(-20.0 * Float64(x - 19.0)) * 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))))))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 4.5)
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((x * (791.0 + (-46.0 * x))) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	else
		tmp = (-20.0 * (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)))))))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 4.5], N[(N[(x - 17.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 16.0), $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[(N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $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 - 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-20.0 * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * 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]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.5

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 97.9%

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

   5. Applied rewrites 97.9%

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-*.f64 18.1%

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

   10. Applied rewrites 18.1%

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

   if 4.5 < x

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 20.8%

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

Alternative 14: 23.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 9:\\ \;\;\;\;\left(380 + -39 \cdot x\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 9.0d0) then
        tmp = (380.0d0 + ((-39.0d0) * x)) * ((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)))))))))))))
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

function code(x)
	tmp = 0.0
	if (x <= 9.0)
		tmp = Float64(Float64(380.0 + Float64(-39.0 * x)) * 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))))))))))))));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, 9.0], N[(N[(380.0 + N[(-39.0 * x), $MachinePrecision]), $MachinePrecision] * 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]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 19.5%

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

   6. Applied rewrites 19.5%

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

   if 9 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 13.7%

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

   4. Applied rewrites 13.7%

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

Alternative 15: 23.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 8.8:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(1835 \cdot x - 21350\right)\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 8.8)
  (*
   (*
    (*
     (- 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))))))))))
    (+ 93024.0 (* x (- (* 1835.0 x) 21350.0))))
   (- x 20.0))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (- (* x (+ 274.0 (* x (- (* 85.0 x) 225.0)))) 120.0)
                 (- x 6.0))
                (- x 7.0))
               (- x 8.0))
              (- x 9.0))
             (- x 10.0))
            (- x 11.0))
           (- x 12.0))
          (- x 13.0))
         (- x 14.0))
        (- x 15.0))
       (- x 16.0))
      (- x 17.0))
     (- x 18.0))
    (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 8.8) {
		tmp = (((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)))))))))) * (93024.0 + (x * ((1835.0 * x) - 21350.0)))) * (x - 20.0);
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 8.8d0) then
        tmp = (((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)))))))))) * (93024.0d0 + (x * ((1835.0d0 * x) - 21350.0d0)))) * (x - 20.0d0)
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 8.8) {
		tmp = (((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)))))))))) * (93024.0 + (x * ((1835.0 * x) - 21350.0)))) * (x - 20.0);
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 8.8:
		tmp = (((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)))))))))) * (93024.0 + (x * ((1835.0 * x) - 21350.0)))) * (x - 20.0)
	else:
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 8.8)
		tmp = Float64(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(93024.0 + Float64(x * Float64(Float64(1835.0 * x) - 21350.0)))) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 8.8)
		tmp = (((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)))))))))) * (93024.0 + (x * ((1835.0 * x) - 21350.0)))) * (x - 20.0);
	else
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 8.8], N[(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[(93024.0 + N[(x * N[(N[(1835.0 * x), $MachinePrecision] - 21350.0), $MachinePrecision]), $MachinePrecision]), $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[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 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%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(93024 + x \cdot \left(1835 \cdot x - 21350\right)\right)}\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + \color{blue}{x \cdot \left(1835 \cdot x - 21350\right)}\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \color{blue}{\left(1835 \cdot x - 21350\right)}\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(1835 \cdot x - \color{blue}{21350}\right)\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 21.7%

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + x \cdot \left(1835 \cdot x - 21350\right)\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 21.7%

      \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(93024 + x \cdot \left(1835 \cdot x - 21350\right)\right)}\right) \cdot \left(x - 20\right) \]

   if 8.8000000000000007 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 13.7%

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

   4. Applied rewrites 13.7%

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

Alternative 16: 21.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 5.9:\\ \;\;\;\;\left(x - 17\right) \cdot \left(\left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(791 \cdot x - 6026\right)\right) \cdot \left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 + x \cdot \left(35 \cdot x - 50\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 5.9)
  (*
   (- x 17.0)
   (*
    (*
     (*
      (*
       (- x 16.0)
       (*
        (*
         (*
          (+ 17160.0 (* x (- (* 791.0 x) 6026.0)))
          (*
           (*
            (* (* (* (- x 4.0) (- x 5.0)) (- x 7.0)) (- x 6.0))
            (* (* (- x 1.0) (- x 2.0)) (- x 3.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 15.0)))
      (- x 19.0))
     (- x 18.0))
    (- x 20.0)))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (* (+ 24.0 (* x (- (* 35.0 x) 50.0))) (- x 5.0))
                 (- x 6.0))
                (- x 7.0))
               (- x 8.0))
              (- x 9.0))
             (- x 10.0))
            (- x 11.0))
           (- x 12.0))
          (- x 13.0))
         (- x 14.0))
        (- x 15.0))
       (- x 16.0))
      (- x 17.0))
     (- x 18.0))
    (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 5.9) {
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	} else {
		tmp = ((((((((((((((((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 5.9d0) then
        tmp = (x - 17.0d0) * (((((x - 16.0d0) * ((((17160.0d0 + (x * ((791.0d0 * x) - 6026.0d0))) * ((((((x - 4.0d0) * (x - 5.0d0)) * (x - 7.0d0)) * (x - 6.0d0)) * (((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 15.0d0))) * (x - 19.0d0)) * (x - 18.0d0)) * (x - 20.0d0))
    else
        tmp = ((((((((((((((((24.0d0 + (x * ((35.0d0 * x) - 50.0d0))) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 5.9) {
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	} else {
		tmp = ((((((((((((((((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 5.9:
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0))
	else:
		tmp = ((((((((((((((((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 5.9)
		tmp = Float64(Float64(x - 17.0) * Float64(Float64(Float64(Float64(Float64(x - 16.0) * Float64(Float64(Float64(Float64(17160.0 + Float64(x * Float64(Float64(791.0 * x) - 6026.0))) * Float64(Float64(Float64(Float64(Float64(Float64(x - 4.0) * Float64(x - 5.0)) * Float64(x - 7.0)) * Float64(x - 6.0)) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 15.0))) * Float64(x - 19.0)) * Float64(x - 18.0)) * Float64(x - 20.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(24.0 + Float64(x * Float64(Float64(35.0 * x) - 50.0))) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 5.9)
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	else
		tmp = ((((((((((((((((24.0 + (x * ((35.0 * x) - 50.0))) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 5.9], N[(N[(x - 17.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 16.0), $MachinePrecision] * N[(N[(N[(N[(17160.0 + N[(x * N[(N[(791.0 * x), $MachinePrecision] - 6026.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $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 - 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(24.0 + N[(x * N[(N[(35.0 * x), $MachinePrecision] - 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.9000000000000004

   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%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 97.9%

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

   5. Applied rewrites 97.9%

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 18.7%

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

   10. Applied rewrites 18.7%

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

   if 5.9000000000000004 < 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

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(24 + x \cdot \left(35 \cdot x - 50\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 + \color{blue}{x \cdot \left(35 \cdot x - 50\right)}\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 + x \cdot \color{blue}{\left(35 \cdot x - 50\right)}\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 + x \cdot \left(35 \cdot x - \color{blue}{50}\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 11.5%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(24 + x \cdot \left(35 \cdot x - 50\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 11.5%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(24 + x \cdot \left(35 \cdot x - 50\right)\right)} \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 21.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 6.9:\\ \;\;\;\;\left(x - 17\right) \cdot \left(\left(\left(\left(\left(x - 16\right) \cdot \left(\left(\left(\left(17160 + x \cdot \left(791 \cdot x - 6026\right)\right) \cdot \left(\left(\left(\left(\left(\left(x - 4\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right)\right) \cdot \left(\left(x - 8\right) \cdot \left(x - 9\right)\right)\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x \cdot \left(274 + x \cdot \left(85 \cdot x - 225\right)\right) - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 6.9)
  (*
   (- x 17.0)
   (*
    (*
     (*
      (*
       (- x 16.0)
       (*
        (*
         (*
          (+ 17160.0 (* x (- (* 791.0 x) 6026.0)))
          (*
           (*
            (* (* (* (- x 4.0) (- x 5.0)) (- x 7.0)) (- x 6.0))
            (* (* (- x 1.0) (- x 2.0)) (- x 3.0)))
           (* (- x 8.0) (- x 9.0))))
         (- x 14.0))
        (- x 15.0)))
      (- x 19.0))
     (- x 18.0))
    (- x 20.0)))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (- (* x (+ 274.0 (* x (- (* 85.0 x) 225.0)))) 120.0)
                 (- x 6.0))
                (- x 7.0))
               (- x 8.0))
              (- x 9.0))
             (- x 10.0))
            (- x 11.0))
           (- x 12.0))
          (- x 13.0))
         (- x 14.0))
        (- x 15.0))
       (- x 16.0))
      (- x 17.0))
     (- x 18.0))
    (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (x <= 6.9) {
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 6.9d0) then
        tmp = (x - 17.0d0) * (((((x - 16.0d0) * ((((17160.0d0 + (x * ((791.0d0 * x) - 6026.0d0))) * ((((((x - 4.0d0) * (x - 5.0d0)) * (x - 7.0d0)) * (x - 6.0d0)) * (((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0))) * ((x - 8.0d0) * (x - 9.0d0)))) * (x - 14.0d0)) * (x - 15.0d0))) * (x - 19.0d0)) * (x - 18.0d0)) * (x - 20.0d0))
    else
        tmp = ((((((((((((((((x * (274.0d0 + (x * ((85.0d0 * x) - 225.0d0)))) - 120.0d0) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 6.9) {
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	} else {
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 6.9:
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0))
	else:
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 6.9)
		tmp = Float64(Float64(x - 17.0) * Float64(Float64(Float64(Float64(Float64(x - 16.0) * Float64(Float64(Float64(Float64(17160.0 + Float64(x * Float64(Float64(791.0 * x) - 6026.0))) * Float64(Float64(Float64(Float64(Float64(Float64(x - 4.0) * Float64(x - 5.0)) * Float64(x - 7.0)) * Float64(x - 6.0)) * Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0))) * Float64(Float64(x - 8.0) * Float64(x - 9.0)))) * Float64(x - 14.0)) * Float64(x - 15.0))) * Float64(x - 19.0)) * Float64(x - 18.0)) * Float64(x - 20.0)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * Float64(274.0 + Float64(x * Float64(Float64(85.0 * x) - 225.0)))) - 120.0) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 6.9)
		tmp = (x - 17.0) * (((((x - 16.0) * ((((17160.0 + (x * ((791.0 * x) - 6026.0))) * ((((((x - 4.0) * (x - 5.0)) * (x - 7.0)) * (x - 6.0)) * (((x - 1.0) * (x - 2.0)) * (x - 3.0))) * ((x - 8.0) * (x - 9.0)))) * (x - 14.0)) * (x - 15.0))) * (x - 19.0)) * (x - 18.0)) * (x - 20.0));
	else
		tmp = ((((((((((((((((x * (274.0 + (x * ((85.0 * x) - 225.0)))) - 120.0) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 6.9], N[(N[(x - 17.0), $MachinePrecision] * N[(N[(N[(N[(N[(x - 16.0), $MachinePrecision] * N[(N[(N[(N[(17160.0 + N[(x * N[(N[(791.0 * x), $MachinePrecision] - 6026.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(N[(N[(x - 4.0), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $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 - 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x * N[(274.0 + N[(x * N[(N[(85.0 * x), $MachinePrecision] - 225.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 120.0), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.9000000000000004

   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%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 97.9%

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

   5. Applied rewrites 97.9%

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 18.7%

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

   10. Applied rewrites 18.7%

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

   if 6.9000000000000004 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 13.7%

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

   4. Applied rewrites 13.7%

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

Alternative 18: 18.9% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x)
  :precision binary64
  (*
 380.0
 (*
  (- 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)))))))))))))))

C

double code(double x) {
	return 380.0 * ((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)))))))))))));
}

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 = 380.0d0 * ((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)))))))))))))
end function

Java

public static double code(double x) {
	return 380.0 * ((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)))))))))))));
}

Python

def code(x):
	return 380.0 * ((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)))))))))))))

Julia

function code(x)
	return Float64(380.0 * 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))))))))))))))
end

MATLAB

function tmp = code(x)
	tmp = 380.0 * ((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)))))))))))));
end

Wolfram

code[x_] := N[(380.0 * 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]), $MachinePrecision]

Derivation

1. Initial program 97.8%

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

3. Applied rewrites 97.8%

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

4. Taylor expanded in x around 0

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

6. Applied rewrites 18.9%

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

Alternative 19: 18.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 5:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + -21350 \cdot x\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(274 \cdot x - 120\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<= x 5.0)
  (*
   (*
    (*
     (- 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))))))))))
    (+ 93024.0 (* -21350.0 x)))
   (- x 20.0))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (* (* (- (* 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))))

C

double code(double x) {
	double tmp;
	if (x <= 5.0) {
		tmp = (((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)))))))))) * (93024.0 + (-21350.0 * x))) * (x - 20.0);
	} else {
		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);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 5.0d0) then
        tmp = (((x - 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)))))))))) * (93024.0d0 + ((-21350.0d0) * x))) * (x - 20.0d0)
    else
        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)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 5.0) {
		tmp = (((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)))))))))) * (93024.0 + (-21350.0 * x))) * (x - 20.0);
	} else {
		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);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 5.0:
		tmp = (((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)))))))))) * (93024.0 + (-21350.0 * x))) * (x - 20.0)
	else:
		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)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 5.0)
		tmp = Float64(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(93024.0 + Float64(-21350.0 * x))) * Float64(x - 20.0));
	else
		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));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 5.0)
		tmp = (((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)))))))))) * (93024.0 + (-21350.0 * x))) * (x - 20.0);
	else
		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);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 5.0], N[(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[(93024.0 + N[(-21350.0 * x), $MachinePrecision]), $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[(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]]

Derivation

1. Split input into 2 regimes

2. if x < 5

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(93024 + -21350 \cdot x\right)}\right) \cdot \left(x - 20\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + \color{blue}{-21350 \cdot x}\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 11.8%

         \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \left(93024 + -21350 \cdot \color{blue}{x}\right)\right) \cdot \left(x - 20\right) \]

   6. Applied rewrites 11.8%

      \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{\left(93024 + -21350 \cdot x\right)}\right) \cdot \left(x - 20\right) \]

   if 5 < x

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 12.9%

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

   4. Applied rewrites 12.9%

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

Alternative 20: 17.0% accurate, 1.2× speedup

Math

\[\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot 93024\right) \cdot \left(x - 20\right) \]

FPCore

(FPCore (x)
  :precision binary64
  (*
 (*
  (*
   (- 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))))))))))
  93024.0)
 (- x 20.0)))

C

double code(double x) {
	return (((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)))))))))) * 93024.0) * (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 - 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)))))))))) * 93024.0d0) * (x - 20.0d0)
end function

Java

public static double code(double x) {
	return (((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)))))))))) * 93024.0) * (x - 20.0);
}

Python

def code(x):
	return (((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)))))))))) * 93024.0) * (x - 20.0)

Julia

function code(x)
	return Float64(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)))))))))) * 93024.0) * Float64(x - 20.0))
end

MATLAB

function tmp = code(x)
	tmp = (((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)))))))))) * 93024.0) * (x - 20.0);
end

Wolfram

code[x_] := N[(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] * 93024.0), $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%

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

4. Taylor expanded in x around 0

   \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{93024}\right) \cdot \left(x - 20\right) \]
5. Step-by-step derivation

6. Applied rewrites 17.0%

   \[\leadsto \left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot \left(\left(\left(x - 12\right) \cdot \left(x - 11\right)\right) \cdot \left(\left(x - 10\right) \cdot \left(\left(\left(x - 9\right) \cdot \left(x - 8\right)\right) \cdot \left(\left(x - 7\right) \cdot \left(\left(\left(x - 6\right) \cdot \left(\left(x - 3\right) \cdot \left(\left(x - 2\right) \cdot \left(x - 1\right)\right)\right)\right) \cdot \left(\left(x - 5\right) \cdot \left(x - 4\right)\right)\right)\right)\right)\right)\right)\right)\right)\right) \cdot \color{blue}{93024}\right) \cdot \left(x - 20\right) \]
7. Add Preprocessing

Alternative 21: 14.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 613000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(13068 \cdot x - 5040\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     613000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (* (* (- (* 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)) <= 613000000000.0) {
		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)) <= 613000000000.0d0) 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)) <= 613000000000.0) {
		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)) <= 613000000000.0:
		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)) <= 613000000000.0)
		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)) <= 613000000000.0)
		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], 613000000000.0], 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))) < 6.13e11

   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 6.13e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-pow.f64 8.0%

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

   4. Applied rewrites 8.0%

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

Alternative 22: 14.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 200000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left({x}^{10} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     200000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (- (* 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)) <= 200000000000.0) {
		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)) <= 200000000000.0d0) 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)) <= 200000000000.0) {
		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)) <= 200000000000.0:
		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)) <= 200000000000.0)
		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)) <= 200000000000.0)
		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], 200000000000.0], 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))) < 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 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.8%

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

   4. Applied rewrites 10.8%

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

   if 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 inf

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

      1. lower-pow.f64 8.0%

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

   4. Applied rewrites 8.0%

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

Alternative 23: 13.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 120000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(40320 \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     120000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (- (* 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)) <= 120000000000.0) {
		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)) <= 120000000000.0d0) 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)) <= 120000000000.0) {
		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)) <= 120000000000.0:
		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)) <= 120000000000.0)
		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)) <= 120000000000.0)
		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], 120000000000.0], 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))) < 1.2e11

   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 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.8%

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

   4. Applied rewrites 10.8%

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

   if 1.2e11 < (*.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

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

   4. Applied rewrites 8.1%

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

Alternative 24: 13.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 400000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(1026576 \cdot x - 362880\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot {x}^{12}\right)\right)\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     400000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (*
           (* (* (- (* 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 15.0) (* (- x 14.0) (* (- x 13.0) (pow x 12.0))))
    (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0))))
   (- 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)) <= 400000000000.0) {
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * pow(x, 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) <= 400000000000.0d0) 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 - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * (x ** 12.0d0)))) * (((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0)))) * (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)) <= 400000000000.0) {
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * Math.pow(x, 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) <= 400000000000.0:
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * math.pow(x, 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) <= 400000000000.0)
		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(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * (x ^ 12.0)))) * Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * 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)) <= 400000000000.0)
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * (x ^ 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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], 400000000000.0], 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[(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] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $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))) < 4e11

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.8%

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

   4. Applied rewrites 10.8%

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

   if 4e11 < (*.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%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.2%

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

   6. Applied rewrites 7.2%

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

Alternative 25: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 20000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + x \cdot \left(12753576 \cdot x - 10628640\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     20000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (- (* 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 (- (* 12753576.0 x) 10628640.0)))
            (- x 11.0))
           (- x 12.0))
          (- 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)) <= 20000000000.0) {
		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 * ((12753576.0 * x) - 10628640.0))) * (x - 11.0)) * (x - 12.0)) * (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)) <= 20000000000.0d0) 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 * ((12753576.0d0 * x) - 10628640.0d0))) * (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)) <= 20000000000.0) {
		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 * ((12753576.0 * x) - 10628640.0))) * (x - 11.0)) * (x - 12.0)) * (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)) <= 20000000000.0:
		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 * ((12753576.0 * x) - 10628640.0))) * (x - 11.0)) * (x - 12.0)) * (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)) <= 20000000000.0)
		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(Float64(3628800.0 + Float64(x * Float64(Float64(12753576.0 * x) - 10628640.0))) * 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)) <= 20000000000.0)
		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 * ((12753576.0 * x) - 10628640.0))) * (x - 11.0)) * (x - 12.0)) * (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], 20000000000.0], 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[(N[(3628800.0 + N[(x * N[(N[(12753576.0 * x), $MachinePrecision] - 10628640.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 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))) < 2e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.2%

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

   7. Applied rewrites 10.2%

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

   if 2e10 < (*.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

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(3628800 + x \cdot \left(12753576 \cdot x - 10628640\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + \color{blue}{x \cdot \left(12753576 \cdot x - 10628640\right)}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + x \cdot \color{blue}{\left(12753576 \cdot x - 10628640\right)}\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + x \cdot \left(12753576 \cdot x - \color{blue}{10628640}\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

      4. lower-*.f64 7.8%

         \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 + x \cdot \left(12753576 \cdot x - 10628640\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]

   4. Applied rewrites 7.8%

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(\left(\left(\color{blue}{\left(3628800 + x \cdot \left(12753576 \cdot x - 10628640\right)\right)} \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 60000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot {x}^{12}\right)\right)\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     60000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (- (* 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 15.0) (* (- x 14.0) (* (- x 13.0) (pow x 12.0))))
    (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0))))
   (- 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)) <= 60000000000.0) {
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * pow(x, 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) <= 60000000000.0d0) 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 - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * (x ** 12.0d0)))) * (((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0)))) * (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)) <= 60000000000.0) {
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * Math.pow(x, 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) <= 60000000000.0:
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * math.pow(x, 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) <= 60000000000.0)
		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(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * (x ^ 12.0)))) * Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * 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)) <= 60000000000.0)
		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 - 15.0) * ((x - 14.0) * ((x - 13.0) * (x ^ 12.0)))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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], 60000000000.0], 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[(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] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $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))) < 6e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.2%

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

   7. Applied rewrites 10.2%

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

   if 6e10 < (*.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%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 7.2%

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

   6. Applied rewrites 7.2%

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

Alternative 27: 13.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq 60000000000:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(120543840 \cdot x - 39916800\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

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))
     60000000000.0)
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (*
          (* (- (* 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))
   -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)) <= 60000000000.0) {
		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)) * -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)) <= 60000000000.0d0) 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)) * (-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)) <= 60000000000.0) {
		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)) * -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)) <= 60000000000.0:
		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)) * -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)) <= 60000000000.0)
		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)) * -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)) <= 60000000000.0)
		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)) * -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], 60000000000.0], 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] * -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))) < 6e10

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 10.2%

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

   7. Applied rewrites 10.2%

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

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 7.8%

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

Alternative 28: 13.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -190000000000:\\ \;\;\;\;\left({x}^{15} \cdot \left(\left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot -20\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<=
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (- x 1.0) (- x 2.0)) (- x 3.0))
                      (- x 4.0))
                     (- x 5.0))
                    (- x 6.0))
                   (- x 7.0))
                  (- x 8.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     -190000000000.0)
  (*
   (*
    (pow x 15.0)
    (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0))))
   (- x 20.0))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* 3628800.0 (- x 11.0)) (- x 12.0)) (- x 13.0))
         (- x 14.0))
        (- x 15.0))
       (- x 16.0))
      (- x 17.0))
     (- x 18.0))
    (- x 19.0))
   -20.0)))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -190000000000.0) {
		tmp = (pow(x, 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
	} else {
		tmp = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-190000000000.0d0)) then
        tmp = ((x ** 15.0d0) * (((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0)))) * (x - 20.0d0)
    else
        tmp = (((((((((3628800.0d0 * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (-20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -190000000000.0) {
		tmp = (Math.pow(x, 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
	} else {
		tmp = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -190000000000.0:
		tmp = (math.pow(x, 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0)
	else:
		tmp = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -190000000000.0)
		tmp = Float64(Float64((x ^ 15.0) * Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(3628800.0 * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * -20.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -190000000000.0)
		tmp = ((x ^ 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
	else
		tmp = (((((((((3628800.0 * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * -20.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -190000000000.0], N[(N[(N[Power[x, 15.0], $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(3628800.0 * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * -20.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -1.9e11

   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%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 9.0%

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

   6. Applied rewrites 9.0%

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

   if -1.9e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 7.8%

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

Alternative 29: 13.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -190000000000:\\ \;\;\;\;\left({x}^{15} \cdot \left(\left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\left(\left(\left(3628800 \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot -17\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<=
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (- x 1.0) (- x 2.0)) (- x 3.0))
                      (- x 4.0))
                     (- x 5.0))
                    (- x 6.0))
                   (- x 7.0))
                  (- x 8.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     -190000000000.0)
  (*
   (*
    (pow x 15.0)
    (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0))))
   (- x 20.0))
  (*
   (*
    (*
     (*
      (*
       (*
        (*
         (* (* (* 3628800.0 (- x 11.0)) (- x 12.0)) (- x 13.0))
         (- x 14.0))
        (- x 15.0))
       (- x 16.0))
      -17.0)
     (- x 18.0))
    (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -190000000000.0) {
		tmp = (pow(x, 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) * -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)) <= (-190000000000.0d0)) then
        tmp = ((x ** 15.0d0) * (((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0)))) * (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)) * (-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)) <= -190000000000.0) {
		tmp = (Math.pow(x, 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) * -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)) <= -190000000000.0:
		tmp = (math.pow(x, 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) * -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)) <= -190000000000.0)
		tmp = Float64(Float64((x ^ 15.0) * Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * 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)) * -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)) <= -190000000000.0)
		tmp = ((x ^ 15.0) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (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)) * -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], -190000000000.0], N[(N[(N[Power[x, 15.0], $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $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] * -17.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64))) < -1.9e11

   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%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 9.0%

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

   6. Applied rewrites 9.0%

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

   if -1.9e11 < (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 2 binary64))) (-.f64 x #s(literal 3 binary64))) (-.f64 x #s(literal 4 binary64))) (-.f64 x #s(literal 5 binary64))) (-.f64 x #s(literal 6 binary64))) (-.f64 x #s(literal 7 binary64))) (-.f64 x #s(literal 8 binary64))) (-.f64 x #s(literal 9 binary64))) (-.f64 x #s(literal 10 binary64))) (-.f64 x #s(literal 11 binary64))) (-.f64 x #s(literal 12 binary64))) (-.f64 x #s(literal 13 binary64))) (-.f64 x #s(literal 14 binary64))) (-.f64 x #s(literal 15 binary64))) (-.f64 x #s(literal 16 binary64))) (-.f64 x #s(literal 17 binary64))) (-.f64 x #s(literal 18 binary64))) (-.f64 x #s(literal 19 binary64))) (-.f64 x #s(literal 20 binary64)))

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 7.3%

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

Alternative 30: 13.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left({x}^{15} \cdot t\_0\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot 479001600\right)\right)\right) \cdot t\_0\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0)))))
  (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))
       -20000000000.0)
    (* (* (pow x 15.0) t_0) (- x 20.0))
    (*
     (* (* (- x 15.0) (* (- x 14.0) (* (- x 13.0) 479001600.0))) t_0)
     (- x 20.0)))))

C

double code(double x) {
	double t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0));
	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)) <= -20000000000.0) {
		tmp = (pow(x, 15.0) * t_0) * (x - 20.0);
	} else {
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_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) :: t_0
    real(8) :: tmp
    t_0 = ((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0))
    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)) <= (-20000000000.0d0)) then
        tmp = ((x ** 15.0d0) * t_0) * (x - 20.0d0)
    else
        tmp = (((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * 479001600.0d0))) * t_0) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0));
	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)) <= -20000000000.0) {
		tmp = (Math.pow(x, 15.0) * t_0) * (x - 20.0);
	} else {
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0))
	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)) <= -20000000000.0:
		tmp = (math.pow(x, 15.0) * t_0) * (x - 20.0)
	else:
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_0) * (x - 20.0)
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))
	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)) <= -20000000000.0)
		tmp = Float64(Float64((x ^ 15.0) * t_0) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * 479001600.0))) * t_0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0));
	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)) <= -20000000000.0)
		tmp = ((x ^ 15.0) * t_0) * (x - 20.0);
	else
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $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], -20000000000.0], N[(N[(N[Power[x, 15.0], $MachinePrecision] * t$95$0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * 479001600.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $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))) < -2e10

   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%

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

   4. Taylor expanded in x around inf

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

      1. lower-pow.f64 9.0%

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

   6. Applied rewrites 9.0%

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

   if -2e10 < (*.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%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 7.2%

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

Alternative 31: 13.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(19802759040 \cdot x - 6227020800\right)\right)\right) \cdot t\_0\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(\left(x - 13\right) \cdot 479001600\right)\right)\right) \cdot t\_0\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (let* ((t_0 (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0)))))
  (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))
       -20000000000.0)
    (*
     (*
      (*
       (- x 15.0)
       (* (- x 14.0) (- (* 19802759040.0 x) 6227020800.0)))
      t_0)
     (- x 20.0))
    (*
     (* (* (- x 15.0) (* (- x 14.0) (* (- x 13.0) 479001600.0))) t_0)
     (- x 20.0)))))

C

double code(double x) {
	double t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0));
	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)) <= -20000000000.0) {
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * t_0) * (x - 20.0);
	} else {
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_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) :: t_0
    real(8) :: tmp
    t_0 = ((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0))
    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)) <= (-20000000000.0d0)) then
        tmp = (((x - 15.0d0) * ((x - 14.0d0) * ((19802759040.0d0 * x) - 6227020800.0d0))) * t_0) * (x - 20.0d0)
    else
        tmp = (((x - 15.0d0) * ((x - 14.0d0) * ((x - 13.0d0) * 479001600.0d0))) * t_0) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0));
	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)) <= -20000000000.0) {
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * t_0) * (x - 20.0);
	} else {
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_0) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0))
	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)) <= -20000000000.0:
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * t_0) * (x - 20.0)
	else:
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_0) * (x - 20.0)
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))
	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)) <= -20000000000.0)
		tmp = Float64(Float64(Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(19802759040.0 * x) - 6227020800.0))) * t_0) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(x - 13.0) * 479001600.0))) * t_0) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = ((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0));
	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)) <= -20000000000.0)
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * t_0) * (x - 20.0);
	else
		tmp = (((x - 15.0) * ((x - 14.0) * ((x - 13.0) * 479001600.0))) * t_0) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $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], -20000000000.0], N[(N[(N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(19802759040.0 * x), $MachinePrecision] - 6227020800.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(x - 13.0), $MachinePrecision] * 479001600.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $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))) < -2e10

   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%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.6%

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

   6. Applied rewrites 9.6%

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

   if -2e10 < (*.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%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 7.2%

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

Alternative 32: 13.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(\left(\left(x - 15\right) \cdot \left(\left(x - 14\right) \cdot \left(19802759040 \cdot x - 6227020800\right)\right)\right) \cdot \left(\left(\left(x - 17\right) \cdot \left(x - 16\right)\right) \cdot \left(\left(x - 19\right) \cdot \left(x - 18\right)\right)\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 20\right) \cdot \left(x - 19\right)\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot 87178291200\right)\right)\right)\right)\\ \end{array} \]

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))
     -20000000000.0)
  (*
   (*
    (* (- x 15.0) (* (- x 14.0) (- (* 19802759040.0 x) 6227020800.0)))
    (* (* (- x 17.0) (- x 16.0)) (* (- x 19.0) (- x 18.0))))
   (- x 20.0))
  (*
   (* (- x 20.0) (- x 19.0))
   (*
    (- x 18.0)
    (* (- x 17.0) (* (- x 16.0) (* (- x 15.0) 87178291200.0)))))))

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)) <= -20000000000.0) {
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
	} else {
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))));
	}
	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)) <= (-20000000000.0d0)) then
        tmp = (((x - 15.0d0) * ((x - 14.0d0) * ((19802759040.0d0 * x) - 6227020800.0d0))) * (((x - 17.0d0) * (x - 16.0d0)) * ((x - 19.0d0) * (x - 18.0d0)))) * (x - 20.0d0)
    else
        tmp = ((x - 20.0d0) * (x - 19.0d0)) * ((x - 18.0d0) * ((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * 87178291200.0d0))))
    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)) <= -20000000000.0) {
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
	} else {
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))));
	}
	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)) <= -20000000000.0:
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0)
	else:
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))))
	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)) <= -20000000000.0)
		tmp = Float64(Float64(Float64(Float64(x - 15.0) * Float64(Float64(x - 14.0) * Float64(Float64(19802759040.0 * x) - 6227020800.0))) * Float64(Float64(Float64(x - 17.0) * Float64(x - 16.0)) * Float64(Float64(x - 19.0) * Float64(x - 18.0)))) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(x - 20.0) * Float64(x - 19.0)) * Float64(Float64(x - 18.0) * Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * 87178291200.0)))));
	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)) <= -20000000000.0)
		tmp = (((x - 15.0) * ((x - 14.0) * ((19802759040.0 * x) - 6227020800.0))) * (((x - 17.0) * (x - 16.0)) * ((x - 19.0) * (x - 18.0)))) * (x - 20.0);
	else
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))));
	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], -20000000000.0], N[(N[(N[(N[(x - 15.0), $MachinePrecision] * N[(N[(x - 14.0), $MachinePrecision] * N[(N[(19802759040.0 * x), $MachinePrecision] - 6227020800.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(x - 17.0), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 19.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * 87178291200.0), $MachinePrecision]), $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))) < -2e10

   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%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.6%

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

   6. Applied rewrites 9.6%

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

   if -2e10 < (*.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%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 6.7%

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

Alternative 33: 13.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \left(x - 20\right) \cdot \left(x - 19\right)\\ \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;t\_0 \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(4339163001600 \cdot x - 1307674368000\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(\left(x - 15\right) \cdot 87178291200\right)\right)\right)\right)\\ \end{array} \]

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))
       -20000000000.0)
    (*
     t_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))))))))

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)) <= -20000000000.0) {
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))));
	} else {
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))));
	}
	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)) <= (-20000000000.0d0)) then
        tmp = t_0 * ((x - 18.0d0) * ((x - 17.0d0) * ((x - 16.0d0) * ((4339163001600.0d0 * x) - 1307674368000.0d0))))
    else
        tmp = t_0 * ((x - 18.0d0) * ((x - 17.0d0) * ((x - 16.0d0) * ((x - 15.0d0) * 87178291200.0d0))))
    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)) <= -20000000000.0) {
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))));
	} else {
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))));
	}
	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)) <= -20000000000.0:
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))))
	else:
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))))
	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)) <= -20000000000.0)
		tmp = Float64(t_0 * Float64(Float64(x - 18.0) * Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(4339163001600.0 * x) - 1307674368000.0)))));
	else
		tmp = Float64(t_0 * Float64(Float64(x - 18.0) * Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(x - 15.0) * 87178291200.0)))));
	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)) <= -20000000000.0)
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))));
	else
		tmp = t_0 * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((x - 15.0) * 87178291200.0))));
	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], -20000000000.0], N[(t$95$0 * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(4339163001600.0 * x), $MachinePrecision] - 1307674368000.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(x - 15.0), $MachinePrecision] * 87178291200.0), $MachinePrecision]), $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))) < -2e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.0%

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

   6. Applied rewrites 9.0%

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

   if -2e10 < (*.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%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 6.7%

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

Alternative 34: 12.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(\left(x - 20\right) \cdot \left(x - 19\right)\right) \cdot \left(\left(x - 18\right) \cdot \left(\left(x - 17\right) \cdot \left(\left(x - 16\right) \cdot \left(4339163001600 \cdot x - 1307674368000\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(20922789888000 \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<=
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (- x 1.0) (- x 2.0)) (- x 3.0))
                      (- x 4.0))
                     (- x 5.0))
                    (- x 6.0))
                   (- x 7.0))
                  (- x 8.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     -20000000000.0)
  (*
   (* (- x 20.0) (- x 19.0))
   (*
    (- x 18.0)
    (*
     (- x 17.0)
     (* (- x 16.0) (- (* 4339163001600.0 x) 1307674368000.0)))))
  (*
   (* (* (* 20922789888000.0 (- x 17.0)) (- x 18.0)) (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0) {
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))));
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-20000000000.0d0)) then
        tmp = ((x - 20.0d0) * (x - 19.0d0)) * ((x - 18.0d0) * ((x - 17.0d0) * ((x - 16.0d0) * ((4339163001600.0d0 * x) - 1307674368000.0d0))))
    else
        tmp = (((20922789888000.0d0 * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0) {
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))));
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0:
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))))
	else:
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -20000000000.0)
		tmp = Float64(Float64(Float64(x - 20.0) * Float64(x - 19.0)) * Float64(Float64(x - 18.0) * Float64(Float64(x - 17.0) * Float64(Float64(x - 16.0) * Float64(Float64(4339163001600.0 * x) - 1307674368000.0)))));
	else
		tmp = Float64(Float64(Float64(Float64(20922789888000.0 * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0)
		tmp = ((x - 20.0) * (x - 19.0)) * ((x - 18.0) * ((x - 17.0) * ((x - 16.0) * ((4339163001600.0 * x) - 1307674368000.0))));
	else
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -20000000000.0], N[(N[(N[(x - 20.0), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 18.0), $MachinePrecision] * N[(N[(x - 17.0), $MachinePrecision] * N[(N[(x - 16.0), $MachinePrecision] * N[(N[(4339163001600.0 * x), $MachinePrecision] - 1307674368000.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(20922789888000.0 * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   4. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 9.0%

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

   6. Applied rewrites 9.0%

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

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 6.2%

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

Alternative 35: 12.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(20922789888000 \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  (if (<=
     (*
      (*
       (*
        (*
         (*
          (*
           (*
            (*
             (*
              (*
               (*
                (*
                 (*
                  (*
                   (*
                    (*
                     (*
                      (* (* (- x 1.0) (- x 2.0)) (- x 3.0))
                      (- x 4.0))
                     (- x 5.0))
                    (- x 6.0))
                   (- x 7.0))
                  (- x 8.0))
                 (- x 9.0))
                (- x 10.0))
               (- x 11.0))
              (- x 12.0))
             (- x 13.0))
            (- x 14.0))
           (- x 15.0))
          (- x 16.0))
         (- x 17.0))
        (- x 18.0))
       (- x 19.0))
      (- x 20.0))
     -20000000000.0)
  (*
   (*
    (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
    (- x 19.0))
   (- x 20.0))
  (*
   (* (* (* 20922789888000.0 (- x 17.0)) (- x 18.0)) (- x 19.0))
   (- x 20.0))))

C

double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((((((((((((((((((((x - 1.0d0) * (x - 2.0d0)) * (x - 3.0d0)) * (x - 4.0d0)) * (x - 5.0d0)) * (x - 6.0d0)) * (x - 7.0d0)) * (x - 8.0d0)) * (x - 9.0d0)) * (x - 10.0d0)) * (x - 11.0d0)) * (x - 12.0d0)) * (x - 13.0d0)) * (x - 14.0d0)) * (x - 15.0d0)) * (x - 16.0d0)) * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)) <= (-20000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (((20922789888000.0d0 * (x - 17.0d0)) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x - 1.0) * Float64(x - 2.0)) * Float64(x - 3.0)) * Float64(x - 4.0)) * Float64(x - 5.0)) * Float64(x - 6.0)) * Float64(x - 7.0)) * Float64(x - 8.0)) * Float64(x - 9.0)) * Float64(x - 10.0)) * Float64(x - 11.0)) * Float64(x - 12.0)) * Float64(x - 13.0)) * Float64(x - 14.0)) * Float64(x - 15.0)) * Float64(x - 16.0)) * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0)) <= -20000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(Float64(Float64(20922789888000.0 * Float64(x - 17.0)) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((((((((((((((((((((x - 1.0) * (x - 2.0)) * (x - 3.0)) * (x - 4.0)) * (x - 5.0)) * (x - 6.0)) * (x - 7.0)) * (x - 8.0)) * (x - 9.0)) * (x - 10.0)) * (x - 11.0)) * (x - 12.0)) * (x - 13.0)) * (x - 14.0)) * (x - 15.0)) * (x - 16.0)) * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)) <= -20000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (((20922789888000.0 * (x - 17.0)) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] * N[(x - 4.0), $MachinePrecision]), $MachinePrecision] * N[(x - 5.0), $MachinePrecision]), $MachinePrecision] * N[(x - 6.0), $MachinePrecision]), $MachinePrecision] * N[(x - 7.0), $MachinePrecision]), $MachinePrecision] * N[(x - 8.0), $MachinePrecision]), $MachinePrecision] * N[(x - 9.0), $MachinePrecision]), $MachinePrecision] * N[(x - 10.0), $MachinePrecision]), $MachinePrecision] * N[(x - 11.0), $MachinePrecision]), $MachinePrecision] * N[(x - 12.0), $MachinePrecision]), $MachinePrecision] * N[(x - 13.0), $MachinePrecision]), $MachinePrecision] * N[(x - 14.0), $MachinePrecision]), $MachinePrecision] * N[(x - 15.0), $MachinePrecision]), $MachinePrecision] * N[(x - 16.0), $MachinePrecision]), $MachinePrecision] * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], -20000000000.0], N[(N[(N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(20922789888000.0 * N[(x - 17.0), $MachinePrecision]), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   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 8.7%

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

   4. Applied rewrites 8.7%

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

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(\left(\left(\color{blue}{20922789888000} \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 6.2%

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

Alternative 36: 12.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(\left(\left(1223405590579200 \cdot x - 355687428096000\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 17\right) \cdot \left(\left(-397533007872000 \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right)\\ \end{array} \]

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))
     -20000000000.0)
  (*
   (*
    (* (- (* 1223405590579200.0 x) 355687428096000.0) (- x 18.0))
    (- x 19.0))
   (- x 20.0))
  (* (- x 17.0) (* (* -397533007872000.0 (- x 18.0)) (- 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)) <= -20000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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)) <= (-20000000000.0d0)) then
        tmp = ((((1223405590579200.0d0 * x) - 355687428096000.0d0) * (x - 18.0d0)) * (x - 19.0d0)) * (x - 20.0d0)
    else
        tmp = (x - 17.0d0) * (((-397533007872000.0d0) * (x - 18.0d0)) * (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)) <= -20000000000.0) {
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	} else {
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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)) <= -20000000000.0:
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0)
	else:
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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)) <= -20000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(1223405590579200.0 * x) - 355687428096000.0) * Float64(x - 18.0)) * Float64(x - 19.0)) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(x - 17.0) * Float64(Float64(-397533007872000.0 * Float64(x - 18.0)) * 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)) <= -20000000000.0)
		tmp = ((((1223405590579200.0 * x) - 355687428096000.0) * (x - 18.0)) * (x - 19.0)) * (x - 20.0);
	else
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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], -20000000000.0], N[(N[(N[(N[(N[(1223405590579200.0 * x), $MachinePrecision] - 355687428096000.0), $MachinePrecision] * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 19.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - 17.0), $MachinePrecision] * N[(N[(-397533007872000.0 * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $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))) < -2e10

   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 8.7%

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

   4. Applied rewrites 8.7%

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

   if -2e10 < (*.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%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 97.9%

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

   5. Applied rewrites 97.9%

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

      \[\leadsto \left(x - 17\right) \cdot \left(\left(\color{blue}{-397533007872000} \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 6.0%

       \[\leadsto \left(x - 17\right) \cdot \left(\left(\color{blue}{-397533007872000} \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 37: 12.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 17\right) \cdot \left(\left(-397533007872000 \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right)\\ \end{array} \]

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))
     -20000000000.0)
  (* (- (* 431565146817638400.0 x) 121645100408832000.0) (- x 20.0))
  (* (- x 17.0) (* (* -397533007872000.0 (- x 18.0)) (- 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)) <= -20000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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)) <= (-20000000000.0d0)) then
        tmp = ((431565146817638400.0d0 * x) - 121645100408832000.0d0) * (x - 20.0d0)
    else
        tmp = (x - 17.0d0) * (((-397533007872000.0d0) * (x - 18.0d0)) * (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)) <= -20000000000.0) {
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	} else {
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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)) <= -20000000000.0:
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0)
	else:
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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)) <= -20000000000.0)
		tmp = Float64(Float64(Float64(431565146817638400.0 * x) - 121645100408832000.0) * Float64(x - 20.0));
	else
		tmp = Float64(Float64(x - 17.0) * Float64(Float64(-397533007872000.0 * Float64(x - 18.0)) * 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)) <= -20000000000.0)
		tmp = ((431565146817638400.0 * x) - 121645100408832000.0) * (x - 20.0);
	else
		tmp = (x - 17.0) * ((-397533007872000.0 * (x - 18.0)) * (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], -20000000000.0], N[(N[(N[(431565146817638400.0 * x), $MachinePrecision] - 121645100408832000.0), $MachinePrecision] * N[(x - 20.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - 17.0), $MachinePrecision] * N[(N[(-397533007872000.0 * N[(x - 18.0), $MachinePrecision]), $MachinePrecision] * N[(x - 20.0), $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))) < -2e10

   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 8.3%

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

   4. Applied rewrites 8.3%

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

   if -2e10 < (*.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%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 97.9%

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

   5. Applied rewrites 97.9%

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

      \[\leadsto \left(x - 17\right) \cdot \left(\left(\color{blue}{-397533007872000} \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 6.0%

       \[\leadsto \left(x - 17\right) \cdot \left(\left(\color{blue}{-397533007872000} \cdot \left(x - 18\right)\right) \cdot \left(x - 20\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 38: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;\left(6402373705728000 \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right)\\ \end{array} \]

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))
     -20000000000.0)
  (* (- (* 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)) <= -20000000000.0) {
		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)) <= (-20000000000.0d0)) 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)) <= -20000000000.0) {
		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)) <= -20000000000.0:
		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)) <= -20000000000.0)
		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)) <= -20000000000.0)
		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], -20000000000.0], 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))) < -2e10

   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 8.3%

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

   4. Applied rewrites 8.3%

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

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

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 7.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(\color{blue}{6402373705728000} \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 5.9%

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

Alternative 39: 12.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\left(431565146817638400 \cdot x - 121645100408832000\right) \cdot \left(x - 20\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
     -20000000000.0)
  (* (- (* 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)) <= -20000000000.0) {
		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)) <= (-20000000000.0d0)) 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)) <= -20000000000.0) {
		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)) <= -20000000000.0:
		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)) <= -20000000000.0)
		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)) <= -20000000000.0)
		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], -20000000000.0], 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))) < -2e10

   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 8.3%

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

   4. Applied rewrites 8.3%

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

   if -2e10 < (*.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

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

      1. lower-pow.f64 9.3%

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

   4. Applied rewrites 9.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 5.6%

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

Alternative 40: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;-121645100408832000 \cdot \left(x - 20\right)\\ \end{array} \]

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))
     -20000000000.0)
  (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)) <= -20000000000.0) {
		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)) <= -20000000000.0)
		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], -20000000000.0], 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))) < -2e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   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 8.2%

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

   6. Applied rewrites 8.2%

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

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

   8. Applied rewrites 8.2%

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

   if -2e10 < (*.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

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

      1. lower-pow.f64 9.3%

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

   4. Applied rewrites 9.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 5.6%

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

Alternative 41: 12.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;\mathsf{fma}\left(x, -8.7529480367616 \cdot 10^{+18}, 2.43290200817664 \cdot 10^{+18}\right)\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

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))
     -20000000000.0)
  (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)) <= -20000000000.0) {
		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)) <= -20000000000.0)
		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], -20000000000.0], 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))) < -2e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   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 8.2%

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

   6. Applied rewrites 8.2%

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

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

   8. Applied rewrites 8.2%

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

   if -2e10 < (*.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 5.5%

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

Alternative 42: 12.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(x - 1\right) \cdot \left(x - 2\right)\right) \cdot \left(x - 3\right)\right) \cdot \left(x - 4\right)\right) \cdot \left(x - 5\right)\right) \cdot \left(x - 6\right)\right) \cdot \left(x - 7\right)\right) \cdot \left(x - 8\right)\right) \cdot \left(x - 9\right)\right) \cdot \left(x - 10\right)\right) \cdot \left(x - 11\right)\right) \cdot \left(x - 12\right)\right) \cdot \left(x - 13\right)\right) \cdot \left(x - 14\right)\right) \cdot \left(x - 15\right)\right) \cdot \left(x - 16\right)\right) \cdot \left(x - 17\right)\right) \cdot \left(x - 18\right)\right) \cdot \left(x - 19\right)\right) \cdot \left(x - 20\right) \leq -20000000000:\\ \;\;\;\;-8.7529480367616 \cdot 10^{+18} \cdot x\\ \mathbf{else}:\\ \;\;\;\;2.43290200817664 \cdot 10^{+18}\\ \end{array} \]

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))
     -20000000000.0)
  (* -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)) <= -20000000000.0) {
		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)) <= (-20000000000.0d0)) 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)) <= -20000000000.0) {
		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)) <= -20000000000.0:
		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)) <= -20000000000.0)
		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)) <= -20000000000.0)
		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], -20000000000.0], 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))) < -2e10

   1. Initial program 97.8%

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

   3. Applied rewrites 97.8%

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

   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 8.2%

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

   6. Applied rewrites 8.2%

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

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

   8. Applied rewrites 8.2%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 8.2%

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

   11. Applied rewrites 8.2%

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

   if -2e10 < (*.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 5.5%

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

Alternative 43: 5.5% 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 5.5%

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

Reproduce

herbie shell --seed 2025218 
(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)))