Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, A

Percentage Accurate: 95.1% → 98.3%

Time: 3.5s

Alternatives: 10

Speedup: 0.1×

• 72.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.1% accurate, 1.0× speedup

Math

\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_2\right)\\ \mathbf{if}\;t\_3 \leq 2 \cdot 10^{-66}:\\ \;\;\;\;\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\left(t\_3 \cdot t\_4\right) \cdot 9\right) \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(t\_4 \cdot t\_1\right) \cdot 9\right) \cdot t\_3\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmin (fmin y z) t))
       (t_2 (fmax (fmin y z) t))
       (t_3 (fmin (fmax y z) t_2))
       (t_4 (fmax (fmax y z) t_2)))
  (if (<= t_3 2e-66)
    (- (- (+ x x) (* (* -27.0 a) b)) (* (* (* t_3 t_4) 9.0) t_1))
    (+ (- (* x 2.0) (* (* (* t_4 t_1) 9.0) t_3)) (* (* a 27.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmin(fmin(y, z), t);
	double t_2 = fmax(fmin(y, z), t);
	double t_3 = fmin(fmax(y, z), t_2);
	double t_4 = fmax(fmax(y, z), t_2);
	double tmp;
	if (t_3 <= 2e-66) {
		tmp = ((x + x) - ((-27.0 * a) * b)) - (((t_3 * t_4) * 9.0) * t_1);
	} else {
		tmp = ((x * 2.0) - (((t_4 * t_1) * 9.0) * t_3)) + ((a * 27.0) * b);
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = fmin(fmin(y, z), t)
    t_2 = fmax(fmin(y, z), t)
    t_3 = fmin(fmax(y, z), t_2)
    t_4 = fmax(fmax(y, z), t_2)
    if (t_3 <= 2d-66) then
        tmp = ((x + x) - (((-27.0d0) * a) * b)) - (((t_3 * t_4) * 9.0d0) * t_1)
    else
        tmp = ((x * 2.0d0) - (((t_4 * t_1) * 9.0d0) * t_3)) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmin(fmin(y, z), t);
	double t_2 = fmax(fmin(y, z), t);
	double t_3 = fmin(fmax(y, z), t_2);
	double t_4 = fmax(fmax(y, z), t_2);
	double tmp;
	if (t_3 <= 2e-66) {
		tmp = ((x + x) - ((-27.0 * a) * b)) - (((t_3 * t_4) * 9.0) * t_1);
	} else {
		tmp = ((x * 2.0) - (((t_4 * t_1) * 9.0) * t_3)) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = fmin(fmin(y, z), t)
	t_2 = fmax(fmin(y, z), t)
	t_3 = fmin(fmax(y, z), t_2)
	t_4 = fmax(fmax(y, z), t_2)
	tmp = 0
	if t_3 <= 2e-66:
		tmp = ((x + x) - ((-27.0 * a) * b)) - (((t_3 * t_4) * 9.0) * t_1)
	else:
		tmp = ((x * 2.0) - (((t_4 * t_1) * 9.0) * t_3)) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = fmin(fmin(y, z), t)
	t_2 = fmax(fmin(y, z), t)
	t_3 = fmin(fmax(y, z), t_2)
	t_4 = fmax(fmax(y, z), t_2)
	tmp = 0.0
	if (t_3 <= 2e-66)
		tmp = Float64(Float64(Float64(x + x) - Float64(Float64(-27.0 * a) * b)) - Float64(Float64(Float64(t_3 * t_4) * 9.0) * t_1));
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(t_4 * t_1) * 9.0) * t_3)) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = min(min(y, z), t);
	t_2 = max(min(y, z), t);
	t_3 = min(max(y, z), t_2);
	t_4 = max(max(y, z), t_2);
	tmp = 0.0;
	if (t_3 <= 2e-66)
		tmp = ((x + x) - ((-27.0 * a) * b)) - (((t_3 * t_4) * 9.0) * t_1);
	else
		tmp = ((x * 2.0) - (((t_4 * t_1) * 9.0) * t_3)) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[y, z], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[y, z], $MachinePrecision], t$95$2], $MachinePrecision]}, If[LessEqual[t$95$3, 2e-66], N[(N[(N[(x + x), $MachinePrecision] - N[(N[(-27.0 * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t$95$3 * t$95$4), $MachinePrecision] * 9.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(t$95$4 * t$95$1), $MachinePrecision] * 9.0), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < 2e-66

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   if 2e-66 < z

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t}\right) + \left(a \cdot 27\right) \cdot b \]

      2. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. associate-*r* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right) \cdot z}\right) + \left(a \cdot 27\right) \cdot b \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(t \cdot \left(y \cdot 9\right)\right) \cdot z}\right) + \left(a \cdot 27\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \left(t \cdot \color{blue}{\left(y \cdot 9\right)}\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      7. associate-*r* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(t \cdot y\right) \cdot 9\right)} \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(t \cdot y\right) \cdot 9\right)} \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      9. lower-*.f64 94.0%

         \[\leadsto \left(x \cdot 2 - \left(\color{blue}{\left(t \cdot y\right)} \cdot 9\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

   3. Applied rewrites 94.0%

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(t \cdot y\right) \cdot 9\right) \cdot z}\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \left(x + x\right) - \left(-27 \cdot a\right) \cdot b\\ t_2 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_3 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_4 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_3\right)\\ t_5 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_3\right)\\ \mathbf{if}\;t\_4 \leq 10000:\\ \;\;\;\;t\_1 - \left(\left(t\_4 \cdot t\_5\right) \cdot 9\right) \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\_5 \cdot \left(t\_4 \cdot \left(9 \cdot t\_2\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (- (+ x x) (* (* -27.0 a) b)))
       (t_2 (fmin (fmin y z) t))
       (t_3 (fmax (fmin y z) t))
       (t_4 (fmin (fmax y z) t_3))
       (t_5 (fmax (fmax y z) t_3)))
  (if (<= t_4 10000.0)
    (- t_1 (* (* (* t_4 t_5) 9.0) t_2))
    (- t_1 (* t_5 (* t_4 (* 9.0 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + x) - ((-27.0 * a) * b);
	double t_2 = fmin(fmin(y, z), t);
	double t_3 = fmax(fmin(y, z), t);
	double t_4 = fmin(fmax(y, z), t_3);
	double t_5 = fmax(fmax(y, z), t_3);
	double tmp;
	if (t_4 <= 10000.0) {
		tmp = t_1 - (((t_4 * t_5) * 9.0) * t_2);
	} else {
		tmp = t_1 - (t_5 * (t_4 * (9.0 * t_2)));
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (x + x) - (((-27.0d0) * a) * b)
    t_2 = fmin(fmin(y, z), t)
    t_3 = fmax(fmin(y, z), t)
    t_4 = fmin(fmax(y, z), t_3)
    t_5 = fmax(fmax(y, z), t_3)
    if (t_4 <= 10000.0d0) then
        tmp = t_1 - (((t_4 * t_5) * 9.0d0) * t_2)
    else
        tmp = t_1 - (t_5 * (t_4 * (9.0d0 * t_2)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + x) - ((-27.0 * a) * b);
	double t_2 = fmin(fmin(y, z), t);
	double t_3 = fmax(fmin(y, z), t);
	double t_4 = fmin(fmax(y, z), t_3);
	double t_5 = fmax(fmax(y, z), t_3);
	double tmp;
	if (t_4 <= 10000.0) {
		tmp = t_1 - (((t_4 * t_5) * 9.0) * t_2);
	} else {
		tmp = t_1 - (t_5 * (t_4 * (9.0 * t_2)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + x) - ((-27.0 * a) * b)
	t_2 = fmin(fmin(y, z), t)
	t_3 = fmax(fmin(y, z), t)
	t_4 = fmin(fmax(y, z), t_3)
	t_5 = fmax(fmax(y, z), t_3)
	tmp = 0
	if t_4 <= 10000.0:
		tmp = t_1 - (((t_4 * t_5) * 9.0) * t_2)
	else:
		tmp = t_1 - (t_5 * (t_4 * (9.0 * t_2)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + x) - Float64(Float64(-27.0 * a) * b))
	t_2 = fmin(fmin(y, z), t)
	t_3 = fmax(fmin(y, z), t)
	t_4 = fmin(fmax(y, z), t_3)
	t_5 = fmax(fmax(y, z), t_3)
	tmp = 0.0
	if (t_4 <= 10000.0)
		tmp = Float64(t_1 - Float64(Float64(Float64(t_4 * t_5) * 9.0) * t_2));
	else
		tmp = Float64(t_1 - Float64(t_5 * Float64(t_4 * Float64(9.0 * t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + x) - ((-27.0 * a) * b);
	t_2 = min(min(y, z), t);
	t_3 = max(min(y, z), t);
	t_4 = min(max(y, z), t_3);
	t_5 = max(max(y, z), t_3);
	tmp = 0.0;
	if (t_4 <= 10000.0)
		tmp = t_1 - (((t_4 * t_5) * 9.0) * t_2);
	else
		tmp = t_1 - (t_5 * (t_4 * (9.0 * t_2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + x), $MachinePrecision] - N[(N[(-27.0 * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Max[y, z], $MachinePrecision], t$95$3], $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Max[y, z], $MachinePrecision], t$95$3], $MachinePrecision]}, If[LessEqual[t$95$4, 10000.0], N[(t$95$1 - N[(N[(N[(t$95$4 * t$95$5), $MachinePrecision] * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(t$95$5 * N[(t$95$4 * N[(9.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < 1e4

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   if 1e4 < z

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 96.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\mathsf{min}\left(y, t\right) \cdot 9\right) \cdot z \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \mathsf{max}\left(y, t\right) \cdot \left(z \cdot \left(9 \cdot \mathsf{min}\left(y, t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(\mathsf{min}\left(y, t\right) \cdot \mathsf{max}\left(y, t\right)\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= (* (* (fmin y t) 9.0) z) 2e+305)
  (-
   (- (+ x x) (* (* -27.0 a) b))
   (* (fmax y t) (* z (* 9.0 (fmin y t)))))
  (+ (* -9.0 (* (* (fmin y t) (fmax y t)) z)) (* (* a 27.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((fmin(y, t) * 9.0) * z) <= 2e+305) {
		tmp = ((x + x) - ((-27.0 * a) * b)) - (fmax(y, t) * (z * (9.0 * fmin(y, t))));
	} else {
		tmp = (-9.0 * ((fmin(y, t) * fmax(y, t)) * z)) + ((a * 27.0) * b);
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((fmin(y, t) * 9.0d0) * z) <= 2d+305) then
        tmp = ((x + x) - (((-27.0d0) * a) * b)) - (fmax(y, t) * (z * (9.0d0 * fmin(y, t))))
    else
        tmp = ((-9.0d0) * ((fmin(y, t) * fmax(y, t)) * z)) + ((a * 27.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((fmin(y, t) * 9.0) * z) <= 2e+305) {
		tmp = ((x + x) - ((-27.0 * a) * b)) - (fmax(y, t) * (z * (9.0 * fmin(y, t))));
	} else {
		tmp = (-9.0 * ((fmin(y, t) * fmax(y, t)) * z)) + ((a * 27.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((fmin(y, t) * 9.0) * z) <= 2e+305:
		tmp = ((x + x) - ((-27.0 * a) * b)) - (fmax(y, t) * (z * (9.0 * fmin(y, t))))
	else:
		tmp = (-9.0 * ((fmin(y, t) * fmax(y, t)) * z)) + ((a * 27.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(fmin(y, t) * 9.0) * z) <= 2e+305)
		tmp = Float64(Float64(Float64(x + x) - Float64(Float64(-27.0 * a) * b)) - Float64(fmax(y, t) * Float64(z * Float64(9.0 * fmin(y, t)))));
	else
		tmp = Float64(Float64(-9.0 * Float64(Float64(fmin(y, t) * fmax(y, t)) * z)) + Float64(Float64(a * 27.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((min(y, t) * 9.0) * z) <= 2e+305)
		tmp = ((x + x) - ((-27.0 * a) * b)) - (max(y, t) * (z * (9.0 * min(y, t))));
	else
		tmp = (-9.0 * ((min(y, t) * max(y, t)) * z)) + ((a * 27.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[Min[y, t], $MachinePrecision] * 9.0), $MachinePrecision] * z), $MachinePrecision], 2e+305], N[(N[(N[(x + x), $MachinePrecision] - N[(N[(-27.0 * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - N[(N[Max[y, t], $MachinePrecision] * N[(z * N[(9.0 * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(N[(N[Min[y, t], $MachinePrecision] * N[Max[y, t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1.9999999999999999e305

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

   if 1.9999999999999999e305 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.4%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      2. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* N/A

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right) + \left(a \cdot 27\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      5. lower-*.f64 65.6%

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right) + \left(a \cdot 27\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative N/A

         \[\leadsto -9 \cdot \left(\left(y \cdot t\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 65.6%

         \[\leadsto -9 \cdot \left(\left(y \cdot t\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

   6. Applied rewrites 65.6%

      \[\leadsto -9 \cdot \left(\left(y \cdot t\right) \cdot \color{blue}{z}\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_2 := \mathsf{min}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(y, z\right), t\_1\right)\\ t_4 := \mathsf{min}\left(\mathsf{min}\left(y, z\right), t\right)\\ t_5 := \left(\left(t\_4 \cdot 9\right) \cdot t\_2\right) \cdot t\_3\\ t_6 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_5 \leq -5 \cdot 10^{+31}:\\ \;\;\;\;-9 \cdot \left(t\_3 \cdot \left(t\_4 \cdot t\_2\right)\right) + t\_6\\ \mathbf{elif}\;t\_5 \leq 10^{-88}:\\ \;\;\;\;2 \cdot x + \left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(\left(t\_4 \cdot t\_3\right) \cdot t\_2\right) + t\_6\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (fmax (fmin y z) t))
       (t_2 (fmin (fmax y z) t_1))
       (t_3 (fmax (fmax y z) t_1))
       (t_4 (fmin (fmin y z) t))
       (t_5 (* (* (* t_4 9.0) t_2) t_3))
       (t_6 (* (* a 27.0) b)))
  (if (<= t_5 -5e+31)
    (+ (* -9.0 (* t_3 (* t_4 t_2))) t_6)
    (if (<= t_5 1e-88)
      (+ (* 2.0 x) (* (* 27.0 b) a))
      (+ (* -9.0 (* (* t_4 t_3) t_2)) t_6)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmin(fmax(y, z), t_1);
	double t_3 = fmax(fmax(y, z), t_1);
	double t_4 = fmin(fmin(y, z), t);
	double t_5 = ((t_4 * 9.0) * t_2) * t_3;
	double t_6 = (a * 27.0) * b;
	double tmp;
	if (t_5 <= -5e+31) {
		tmp = (-9.0 * (t_3 * (t_4 * t_2))) + t_6;
	} else if (t_5 <= 1e-88) {
		tmp = (2.0 * x) + ((27.0 * b) * a);
	} else {
		tmp = (-9.0 * ((t_4 * t_3) * t_2)) + t_6;
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = fmax(fmin(y, z), t)
    t_2 = fmin(fmax(y, z), t_1)
    t_3 = fmax(fmax(y, z), t_1)
    t_4 = fmin(fmin(y, z), t)
    t_5 = ((t_4 * 9.0d0) * t_2) * t_3
    t_6 = (a * 27.0d0) * b
    if (t_5 <= (-5d+31)) then
        tmp = ((-9.0d0) * (t_3 * (t_4 * t_2))) + t_6
    else if (t_5 <= 1d-88) then
        tmp = (2.0d0 * x) + ((27.0d0 * b) * a)
    else
        tmp = ((-9.0d0) * ((t_4 * t_3) * t_2)) + t_6
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fmax(fmin(y, z), t);
	double t_2 = fmin(fmax(y, z), t_1);
	double t_3 = fmax(fmax(y, z), t_1);
	double t_4 = fmin(fmin(y, z), t);
	double t_5 = ((t_4 * 9.0) * t_2) * t_3;
	double t_6 = (a * 27.0) * b;
	double tmp;
	if (t_5 <= -5e+31) {
		tmp = (-9.0 * (t_3 * (t_4 * t_2))) + t_6;
	} else if (t_5 <= 1e-88) {
		tmp = (2.0 * x) + ((27.0 * b) * a);
	} else {
		tmp = (-9.0 * ((t_4 * t_3) * t_2)) + t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmin(fmax(y, z), t_1)
	t_3 = fmax(fmax(y, z), t_1)
	t_4 = fmin(fmin(y, z), t)
	t_5 = ((t_4 * 9.0) * t_2) * t_3
	t_6 = (a * 27.0) * b
	tmp = 0
	if t_5 <= -5e+31:
		tmp = (-9.0 * (t_3 * (t_4 * t_2))) + t_6
	elif t_5 <= 1e-88:
		tmp = (2.0 * x) + ((27.0 * b) * a)
	else:
		tmp = (-9.0 * ((t_4 * t_3) * t_2)) + t_6
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = fmax(fmin(y, z), t)
	t_2 = fmin(fmax(y, z), t_1)
	t_3 = fmax(fmax(y, z), t_1)
	t_4 = fmin(fmin(y, z), t)
	t_5 = Float64(Float64(Float64(t_4 * 9.0) * t_2) * t_3)
	t_6 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_5 <= -5e+31)
		tmp = Float64(Float64(-9.0 * Float64(t_3 * Float64(t_4 * t_2))) + t_6);
	elseif (t_5 <= 1e-88)
		tmp = Float64(Float64(2.0 * x) + Float64(Float64(27.0 * b) * a));
	else
		tmp = Float64(Float64(-9.0 * Float64(Float64(t_4 * t_3) * t_2)) + t_6);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = max(min(y, z), t);
	t_2 = min(max(y, z), t_1);
	t_3 = max(max(y, z), t_1);
	t_4 = min(min(y, z), t);
	t_5 = ((t_4 * 9.0) * t_2) * t_3;
	t_6 = (a * 27.0) * b;
	tmp = 0.0;
	if (t_5 <= -5e+31)
		tmp = (-9.0 * (t_3 * (t_4 * t_2))) + t_6;
	elseif (t_5 <= 1e-88)
		tmp = (2.0 * x) + ((27.0 * b) * a);
	else
		tmp = (-9.0 * ((t_4 * t_3) * t_2)) + t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Max[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[y, z], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[Min[N[Min[y, z], $MachinePrecision], t], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 * 9.0), $MachinePrecision] * t$95$2), $MachinePrecision] * t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$5, -5e+31], N[(N[(-9.0 * N[(t$95$3 * N[(t$95$4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision], If[LessEqual[t$95$5, 1e-88], N[(N[(2.0 * x), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(-9.0 * N[(N[(t$95$4 * t$95$3), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e31

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.4%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

   if -5.0000000000000003e31 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999993e-89

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27} \cdot \left(a \cdot b\right) \]

      3. lower-*.f64 N/A

         \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

      4. lower-*.f64 64.3%

         \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

   4. Applied rewrites 64.3%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot x + 27 \cdot \left(b \cdot \color{blue}{a}\right) \]

      4. associate-*r* N/A

         \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

      6. lower-*.f64 64.2%

         \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot a \]

   6. Applied rewrites 64.2%

      \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

   if 9.9999999999999993e-89 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.4%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      2. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*r* N/A

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right) + \left(a \cdot 27\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      5. lower-*.f64 65.6%

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right) + \left(a \cdot 27\right) \cdot b \]

      6. lift-*.f64 N/A

         \[\leadsto -9 \cdot \left(\left(t \cdot y\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      7. *-commutative N/A

         \[\leadsto -9 \cdot \left(\left(y \cdot t\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 65.6%

         \[\leadsto -9 \cdot \left(\left(y \cdot t\right) \cdot z\right) + \left(a \cdot 27\right) \cdot b \]

   6. Applied rewrites 65.6%

      \[\leadsto -9 \cdot \left(\left(y \cdot t\right) \cdot \color{blue}{z}\right) + \left(a \cdot 27\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := -9 \cdot \left(\mathsf{max}\left(y, t\right) \cdot \left(\mathsf{min}\left(y, t\right) \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b\\ t_2 := \left(\left(\mathsf{min}\left(y, t\right) \cdot 9\right) \cdot z\right) \cdot \mathsf{max}\left(y, t\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-88}:\\ \;\;\;\;2 \cdot x + \left(27 \cdot b\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1
        (+ (* -9.0 (* (fmax y t) (* (fmin y t) z))) (* (* a 27.0) b)))
       (t_2 (* (* (* (fmin y t) 9.0) z) (fmax y t))))
  (if (<= t_2 -5e+31)
    t_1
    (if (<= t_2 1e-88) (+ (* 2.0 x) (* (* 27.0 b) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * (fmax(y, t) * (fmin(y, t) * z))) + ((a * 27.0) * b);
	double t_2 = ((fmin(y, t) * 9.0) * z) * fmax(y, t);
	double tmp;
	if (t_2 <= -5e+31) {
		tmp = t_1;
	} else if (t_2 <= 1e-88) {
		tmp = (2.0 * x) + ((27.0 * b) * a);
	} else {
		tmp = t_1;
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-9.0d0) * (fmax(y, t) * (fmin(y, t) * z))) + ((a * 27.0d0) * b)
    t_2 = ((fmin(y, t) * 9.0d0) * z) * fmax(y, t)
    if (t_2 <= (-5d+31)) then
        tmp = t_1
    else if (t_2 <= 1d-88) then
        tmp = (2.0d0 * x) + ((27.0d0 * b) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-9.0 * (fmax(y, t) * (fmin(y, t) * z))) + ((a * 27.0) * b);
	double t_2 = ((fmin(y, t) * 9.0) * z) * fmax(y, t);
	double tmp;
	if (t_2 <= -5e+31) {
		tmp = t_1;
	} else if (t_2 <= 1e-88) {
		tmp = (2.0 * x) + ((27.0 * b) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-9.0 * (fmax(y, t) * (fmin(y, t) * z))) + ((a * 27.0) * b)
	t_2 = ((fmin(y, t) * 9.0) * z) * fmax(y, t)
	tmp = 0
	if t_2 <= -5e+31:
		tmp = t_1
	elif t_2 <= 1e-88:
		tmp = (2.0 * x) + ((27.0 * b) * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-9.0 * Float64(fmax(y, t) * Float64(fmin(y, t) * z))) + Float64(Float64(a * 27.0) * b))
	t_2 = Float64(Float64(Float64(fmin(y, t) * 9.0) * z) * fmax(y, t))
	tmp = 0.0
	if (t_2 <= -5e+31)
		tmp = t_1;
	elseif (t_2 <= 1e-88)
		tmp = Float64(Float64(2.0 * x) + Float64(Float64(27.0 * b) * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-9.0 * (max(y, t) * (min(y, t) * z))) + ((a * 27.0) * b);
	t_2 = ((min(y, t) * 9.0) * z) * max(y, t);
	tmp = 0.0;
	if (t_2 <= -5e+31)
		tmp = t_1;
	elseif (t_2 <= 1e-88)
		tmp = (2.0 * x) + ((27.0 * b) * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-9.0 * N[(N[Max[y, t], $MachinePrecision] * N[(N[Min[y, t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[Min[y, t], $MachinePrecision] * 9.0), $MachinePrecision] * z), $MachinePrecision] * N[Max[y, t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+31], t$95$1, If[LessEqual[t$95$2, 1e-88], N[(N[(2.0 * x), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000003e31 or 9.9999999999999993e-89 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      3. lower-*.f64 66.4%

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b \]

   if -5.0000000000000003e31 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 9.9999999999999993e-89

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27} \cdot \left(a \cdot b\right) \]

      3. lower-*.f64 N/A

         \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

      4. lower-*.f64 64.3%

         \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

   4. Applied rewrites 64.3%

      \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

      3. *-commutative N/A

         \[\leadsto 2 \cdot x + 27 \cdot \left(b \cdot \color{blue}{a}\right) \]

      4. associate-*r* N/A

         \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

      5. lower-*.f64 N/A

         \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

      6. lower-*.f64 64.2%

         \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot a \]

   6. Applied rewrites 64.2%

      \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 64.3% accurate, 1.9× speedup

Math

\[2 \cdot x + \left(27 \cdot b\right) \cdot a \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (* 2.0 x) (* (* 27.0 b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * x) + ((27.0 * b) * a);
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (2.0d0 * x) + ((27.0d0 * b) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * x) + ((27.0 * b) * a);
}

Python

def code(x, y, z, t, a, b):
	return (2.0 * x) + ((27.0 * b) * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(2.0 * x) + Float64(Float64(27.0 * b) * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * x) + ((27.0 * b) * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * x), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.1%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27} \cdot \left(a \cdot b\right) \]

   3. lower-*.f64 N/A

      \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   4. lower-*.f64 64.3%

      \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

4. Applied rewrites 64.3%

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

   3. *-commutative N/A

      \[\leadsto 2 \cdot x + 27 \cdot \left(b \cdot \color{blue}{a}\right) \]

   4. associate-*r* N/A

      \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

   5. lower-*.f64 N/A

      \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]

   6. lower-*.f64 64.2%

      \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot a \]

6. Applied rewrites 64.2%

   \[\leadsto 2 \cdot x + \left(27 \cdot b\right) \cdot \color{blue}{a} \]
7. Add Preprocessing

Alternative 7: 64.2% accurate, 0.2× speedup

Math

\[\left(x + x\right) - \mathsf{max}\left(a, b\right) \cdot \left(\mathsf{min}\left(a, b\right) \cdot -27\right) \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (- (+ x x) (* (fmax a b) (* (fmin a b) -27.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + x) - (fmax(a, b) * (fmin(a, b) * -27.0));
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x + x) - (fmax(a, b) * (fmin(a, b) * (-27.0d0)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + x) - (fmax(a, b) * (fmin(a, b) * -27.0));
}

Python

def code(x, y, z, t, a, b):
	return (x + x) - (fmax(a, b) * (fmin(a, b) * -27.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + x) - Float64(fmax(a, b) * Float64(fmin(a, b) * -27.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + x) - (max(a, b) * (min(a, b) * -27.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + x), $MachinePrecision] - N[(N[Max[a, b], $MachinePrecision] * N[(N[Min[a, b], $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.1%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27} \cdot \left(a \cdot b\right) \]

   3. lower-*.f64 N/A

      \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   4. lower-*.f64 64.3%

      \[\leadsto 2 \cdot x + 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

4. Applied rewrites 64.3%

   \[\leadsto \color{blue}{2 \cdot x + 27 \cdot \left(a \cdot b\right)} \]
5. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto 2 \cdot x + 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   3. fp-cancel-sign-sub-inv N/A

      \[\leadsto 2 \cdot x - \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(a \cdot b\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto 2 \cdot x - \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(a \cdot b\right) \]

   5. count-2-rev N/A

      \[\leadsto \left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(a \cdot b\right) \]

   6. lift-+.f64 N/A

      \[\leadsto \left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(a \cdot b\right) \]

   7. metadata-eval N/A

      \[\leadsto \left(x + x\right) - -27 \cdot \left(\color{blue}{a} \cdot b\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(x + x\right) - -27 \cdot \left(a \cdot \color{blue}{b}\right) \]

   9. associate-*l* N/A

      \[\leadsto \left(x + x\right) - \left(-27 \cdot a\right) \cdot \color{blue}{b} \]

   10. lift-*.f64 N/A

       \[\leadsto \left(x + x\right) - \left(-27 \cdot a\right) \cdot b \]

   11. lift-*.f64 N/A

       \[\leadsto \left(x + x\right) - \left(-27 \cdot a\right) \cdot \color{blue}{b} \]

   12. lift--.f64 64.3%

       \[\leadsto \left(x + x\right) - \color{blue}{\left(-27 \cdot a\right) \cdot b} \]

   13. lift-*.f64 N/A

       \[\leadsto \left(x + x\right) - \left(-27 \cdot a\right) \cdot \color{blue}{b} \]

   14. *-commutative N/A

       \[\leadsto \left(x + x\right) - b \cdot \color{blue}{\left(-27 \cdot a\right)} \]

   15. lower-*.f64 64.3%

       \[\leadsto \left(x + x\right) - b \cdot \color{blue}{\left(-27 \cdot a\right)} \]

   16. lift-*.f64 N/A

       \[\leadsto \left(x + x\right) - b \cdot \left(-27 \cdot \color{blue}{a}\right) \]

   17. *-commutative N/A

       \[\leadsto \left(x + x\right) - b \cdot \left(a \cdot \color{blue}{-27}\right) \]

   18. lower-*.f64 64.3%

       \[\leadsto \left(x + x\right) - b \cdot \left(a \cdot \color{blue}{-27}\right) \]

6. Applied rewrites 64.3%

   \[\leadsto \color{blue}{\left(x + x\right) - b \cdot \left(a \cdot -27\right)} \]
7. Add Preprocessing

Alternative 8: 52.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{min}\left(a, b\right) \cdot 27\right) \cdot \mathsf{max}\left(a, b\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;-1 \cdot \left(-27 \cdot \left(\mathsf{min}\left(a, b\right) \cdot \mathsf{max}\left(a, b\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;-1 \cdot \left(-2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(\mathsf{max}\left(a, b\right) \cdot \left(-27 \cdot \mathsf{min}\left(a, b\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (* (fmin a b) 27.0) (fmax a b))))
  (if (<= t_1 -5e+80)
    (* -1.0 (* -27.0 (* (fmin a b) (fmax a b))))
    (if (<= t_1 10.0)
      (* -1.0 (* -2.0 x))
      (* -1.0 (* (fmax a b) (* -27.0 (fmin a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (fmin(a, b) * 27.0) * fmax(a, b);
	double tmp;
	if (t_1 <= -5e+80) {
		tmp = -1.0 * (-27.0 * (fmin(a, b) * fmax(a, b)));
	} else if (t_1 <= 10.0) {
		tmp = -1.0 * (-2.0 * x);
	} else {
		tmp = -1.0 * (fmax(a, b) * (-27.0 * fmin(a, b)));
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (fmin(a, b) * 27.0d0) * fmax(a, b)
    if (t_1 <= (-5d+80)) then
        tmp = (-1.0d0) * ((-27.0d0) * (fmin(a, b) * fmax(a, b)))
    else if (t_1 <= 10.0d0) then
        tmp = (-1.0d0) * ((-2.0d0) * x)
    else
        tmp = (-1.0d0) * (fmax(a, b) * ((-27.0d0) * fmin(a, b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (fmin(a, b) * 27.0) * fmax(a, b);
	double tmp;
	if (t_1 <= -5e+80) {
		tmp = -1.0 * (-27.0 * (fmin(a, b) * fmax(a, b)));
	} else if (t_1 <= 10.0) {
		tmp = -1.0 * (-2.0 * x);
	} else {
		tmp = -1.0 * (fmax(a, b) * (-27.0 * fmin(a, b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (fmin(a, b) * 27.0) * fmax(a, b)
	tmp = 0
	if t_1 <= -5e+80:
		tmp = -1.0 * (-27.0 * (fmin(a, b) * fmax(a, b)))
	elif t_1 <= 10.0:
		tmp = -1.0 * (-2.0 * x)
	else:
		tmp = -1.0 * (fmax(a, b) * (-27.0 * fmin(a, b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(fmin(a, b) * 27.0) * fmax(a, b))
	tmp = 0.0
	if (t_1 <= -5e+80)
		tmp = Float64(-1.0 * Float64(-27.0 * Float64(fmin(a, b) * fmax(a, b))));
	elseif (t_1 <= 10.0)
		tmp = Float64(-1.0 * Float64(-2.0 * x));
	else
		tmp = Float64(-1.0 * Float64(fmax(a, b) * Float64(-27.0 * fmin(a, b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (min(a, b) * 27.0) * max(a, b);
	tmp = 0.0;
	if (t_1 <= -5e+80)
		tmp = -1.0 * (-27.0 * (min(a, b) * max(a, b)));
	elseif (t_1 <= 10.0)
		tmp = -1.0 * (-2.0 * x);
	else
		tmp = -1.0 * (max(a, b) * (-27.0 * min(a, b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Min[a, b], $MachinePrecision] * 27.0), $MachinePrecision] * N[Max[a, b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+80], N[(-1.0 * N[(-27.0 * N[(N[Min[a, b], $MachinePrecision] * N[Max[a, b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10.0], N[(-1.0 * N[(-2.0 * x), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(N[Max[a, b], $MachinePrecision] * N[(-27.0 * N[Min[a, b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999996e80

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      11. lower-*.f64 82.2%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot \color{blue}{a}\right)\right) \]

   8. Applied rewrites 82.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(-27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

       2. lower-*.f64 35.4%

          \[\leadsto -1 \cdot \left(-27 \cdot \left(a \cdot b\right)\right) \]

   11. Applied rewrites 35.4%

       \[\leadsto -1 \cdot \left(-27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   if -4.9999999999999996e80 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 10

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      11. lower-*.f64 82.2%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot \color{blue}{a}\right)\right) \]

   8. Applied rewrites 82.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \left(-2 \cdot \color{blue}{x}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 30.8%

          \[\leadsto -1 \cdot \left(-2 \cdot x\right) \]

   11. Applied rewrites 30.8%

       \[\leadsto -1 \cdot \left(-2 \cdot \color{blue}{x}\right) \]

   if 10 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      11. lower-*.f64 82.2%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot \color{blue}{a}\right)\right) \]

   8. Applied rewrites 82.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(b \cdot \left(-27 \cdot \color{blue}{a}\right)\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 35.4%

          \[\leadsto -1 \cdot \left(b \cdot \left(-27 \cdot a\right)\right) \]

   11. Applied rewrites 35.4%

       \[\leadsto -1 \cdot \left(b \cdot \left(-27 \cdot \color{blue}{a}\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := -1 \cdot \left(-27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;-1 \cdot \left(-2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (* a 27.0) b)) (t_2 (* -1.0 (* -27.0 (* a b)))))
  (if (<= t_1 -5e+80) t_2 (if (<= t_1 10.0) (* -1.0 (* -2.0 x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = -1.0 * (-27.0 * (a * b));
	double tmp;
	if (t_1 <= -5e+80) {
		tmp = t_2;
	} else if (t_1 <= 10.0) {
		tmp = -1.0 * (-2.0 * x);
	} else {
		tmp = t_2;
	}
	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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = (-1.0d0) * ((-27.0d0) * (a * b))
    if (t_1 <= (-5d+80)) then
        tmp = t_2
    else if (t_1 <= 10.0d0) then
        tmp = (-1.0d0) * ((-2.0d0) * x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = -1.0 * (-27.0 * (a * b));
	double tmp;
	if (t_1 <= -5e+80) {
		tmp = t_2;
	} else if (t_1 <= 10.0) {
		tmp = -1.0 * (-2.0 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = -1.0 * (-27.0 * (a * b))
	tmp = 0
	if t_1 <= -5e+80:
		tmp = t_2
	elif t_1 <= 10.0:
		tmp = -1.0 * (-2.0 * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(-1.0 * Float64(-27.0 * Float64(a * b)))
	tmp = 0.0
	if (t_1 <= -5e+80)
		tmp = t_2;
	elseif (t_1 <= 10.0)
		tmp = Float64(-1.0 * Float64(-2.0 * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = -1.0 * (-27.0 * (a * b));
	tmp = 0.0;
	if (t_1 <= -5e+80)
		tmp = t_2;
	elseif (t_1 <= 10.0)
		tmp = -1.0 * (-2.0 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 * N[(-27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+80], t$95$2, If[LessEqual[t$95$1, 10.0], N[(-1.0 * N[(-2.0 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.9999999999999996e80 or 10 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      11. lower-*.f64 82.2%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot \color{blue}{a}\right)\right) \]

   8. Applied rewrites 82.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

   9. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(-27 \cdot \left(a \cdot \color{blue}{b}\right)\right) \]

       2. lower-*.f64 35.4%

          \[\leadsto -1 \cdot \left(-27 \cdot \left(a \cdot b\right)\right) \]

   11. Applied rewrites 35.4%

       \[\leadsto -1 \cdot \left(-27 \cdot \color{blue}{\left(a \cdot b\right)}\right) \]

   if -4.9999999999999996e80 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 10

   1. Initial program 95.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      3. lift--.f64 N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      5. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      7. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      9. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      11. *-commutative N/A

          \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      12. count-2-rev N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      13. lower-+.f64 N/A

          \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      14. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      15. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      16. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      18. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      19. metadata-eval 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

      20. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

      21. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      22. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

      23. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

      24. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      25. lower-*.f64 95.1%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

      26. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

      27. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

   3. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

      7. associate-*l* N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

      11. associate-*r* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

      13. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

      14. lift-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

      15. associate-*l* N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      16. lower-*.f64 N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

      17. *-commutative N/A

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

      18. lower-*.f64 94.5%

          \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   5. Applied rewrites 94.5%

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

   6. Taylor expanded in b around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27 \cdot a}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27} \cdot a\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      7. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      10. lower-*.f64 N/A

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

      11. lower-*.f64 82.2%

          \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot \color{blue}{a}\right)\right) \]

   8. Applied rewrites 82.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

   9. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \left(-2 \cdot \color{blue}{x}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 30.8%

          \[\leadsto -1 \cdot \left(-2 \cdot x\right) \]

   11. Applied rewrites 30.8%

       \[\leadsto -1 \cdot \left(-2 \cdot \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 30.8% accurate, 3.4× speedup

Math

\[-1 \cdot \left(-2 \cdot x\right) \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (* -1.0 (* -2.0 x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return -1.0 * (-2.0 * x);
}

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, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (-1.0d0) * ((-2.0d0) * x)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return -1.0 * (-2.0 * x);
}

Python

def code(x, y, z, t, a, b):
	return -1.0 * (-2.0 * x)

Julia

function code(x, y, z, t, a, b)
	return Float64(-1.0 * Float64(-2.0 * x))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = -1.0 * (-2.0 * x);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-1.0 * N[(-2.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.1%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

   3. lift--.f64 N/A

      \[\leadsto \left(a \cdot 27\right) \cdot b + \color{blue}{\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]

   4. associate-+r- N/A

      \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

   5. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

   6. +-commutative N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   7. lift-*.f64 N/A

      \[\leadsto \left(x \cdot 2 + \color{blue}{\left(a \cdot 27\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   8. fp-cancel-sign-sub-inv N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   9. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right)} - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   10. lift-*.f64 N/A

       \[\leadsto \left(\color{blue}{x \cdot 2} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   11. *-commutative N/A

       \[\leadsto \left(\color{blue}{2 \cdot x} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   12. count-2-rev N/A

       \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   13. lower-+.f64 N/A

       \[\leadsto \left(\color{blue}{\left(x + x\right)} - \left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   14. lower-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\mathsf{neg}\left(a \cdot 27\right)\right) \cdot b}\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   15. lift-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{a \cdot 27}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   16. *-commutative N/A

       \[\leadsto \left(\left(x + x\right) - \left(\mathsf{neg}\left(\color{blue}{27 \cdot a}\right)\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   17. distribute-lft-neg-in N/A

       \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   18. lower-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \color{blue}{\left(\left(\mathsf{neg}\left(27\right)\right) \cdot a\right)} \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   19. metadata-eval 95.1%

       \[\leadsto \left(\left(x + x\right) - \left(\color{blue}{-27} \cdot a\right) \cdot b\right) - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t \]

   20. lift-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right) \cdot t} \]

   21. *-commutative N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

   22. lower-*.f64 95.1%

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)} \]

   23. lift-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \]

   24. *-commutative N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

   25. lower-*.f64 95.1%

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)} \]

   26. lift-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(y \cdot 9\right)}\right) \]

   27. *-commutative N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \]

3. Applied rewrites 95.1%

   \[\leadsto \color{blue}{\left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{t \cdot \left(z \cdot \left(9 \cdot y\right)\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right) \cdot t} \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot \left(9 \cdot y\right)\right)} \cdot t \]

   4. lift-*.f64 N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot \color{blue}{\left(9 \cdot y\right)}\right) \cdot t \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)} \cdot t \]

   6. lift-*.f64 N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot 9\right)} \cdot y\right) \cdot t \]

   7. associate-*l* N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(z \cdot 9\right) \cdot \left(y \cdot t\right)} \]

   8. *-commutative N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

   10. lift-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(z \cdot 9\right) \cdot \color{blue}{\left(t \cdot y\right)} \]

   11. associate-*r* N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

   12. lower-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right) \cdot y} \]

   13. *-commutative N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(t \cdot \left(z \cdot 9\right)\right)} \cdot y \]

   14. lift-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(t \cdot \color{blue}{\left(z \cdot 9\right)}\right) \cdot y \]

   15. associate-*l* N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

   16. lower-*.f64 N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(t \cdot z\right) \cdot 9\right)} \cdot y \]

   17. *-commutative N/A

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

   18. lower-*.f64 94.5%

       \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \left(\color{blue}{\left(z \cdot t\right)} \cdot 9\right) \cdot y \]

5. Applied rewrites 94.5%

   \[\leadsto \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) - \color{blue}{\left(\left(z \cdot t\right) \cdot 9\right) \cdot y} \]

6. Taylor expanded in b around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]
7. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \color{blue}{\left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)}\right) \]

   3. lower--.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27 \cdot a}\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - \color{blue}{27} \cdot a\right)\right) \]

   5. lower-/.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

   6. lower--.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

   7. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

   8. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

   10. lower-*.f64 N/A

       \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right) \]

   11. lower-*.f64 82.2%

       \[\leadsto -1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot \color{blue}{a}\right)\right) \]

8. Applied rewrites 82.2%

   \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{2 \cdot x - 9 \cdot \left(t \cdot \left(y \cdot z\right)\right)}{b} - 27 \cdot a\right)\right)} \]

9. Taylor expanded in x around inf

   \[\leadsto -1 \cdot \left(-2 \cdot \color{blue}{x}\right) \]
10. Step-by-step derivation

    1. lower-*.f64 30.8%

       \[\leadsto -1 \cdot \left(-2 \cdot x\right) \]

11. Applied rewrites 30.8%

    \[\leadsto -1 \cdot \left(-2 \cdot \color{blue}{x}\right) \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64
  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))