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

Percentage Accurate: 95.8% → 98.8%

Time: 3.9s

Alternatives: 5

Speedup: N/A×

• 26.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

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: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

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: 98.8% accurate, N/A× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-91}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(-9 \cdot t, z \cdot y, 2 \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1e-91)
   (+ (- (* x 2.0) (* (* t y) (* z 9.0))) (* (* a 27.0) b))
   (fma (* b 27.0) a (fma (* -9.0 t) (* z y) (* 2.0 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e-91) {
		tmp = ((x * 2.0) - ((t * y) * (z * 9.0))) + ((a * 27.0) * b);
	} else {
		tmp = fma((b * 27.0), a, fma((-9.0 * t), (z * y), (2.0 * x)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1e-91)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(t * y) * Float64(z * 9.0))) + Float64(Float64(a * 27.0) * b));
	else
		tmp = fma(Float64(b * 27.0), a, fma(Float64(-9.0 * t), Float64(z * y), Float64(2.0 * x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1e-91], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(-9.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000002e-91

   1. Initial program 94.0%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. 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. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 96.5

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

   4. Applied rewrites 96.5%

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

   if 1.00000000000000002e-91 < t

   1. Initial program 96.1%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. 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. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. *-commutative N/A

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

      17. associate-*r* N/A

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

      18. cancel-sign-sub-inv N/A

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

   4. Applied rewrites 98.6%

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

Alternative 2: 96.3% accurate, N/A× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, 2 \cdot x\right)\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* b 27.0) a (fma (* (* z t) -9.0) y (* 2.0 x))))

C

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(b * 27.0), a, fma(Float64(Float64(z * t) * -9.0), y, Float64(2.0 * x)))
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(N[(z * t), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(2.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing
3. 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. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 95.6

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

4. Applied rewrites 95.6%

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

6. Applied rewrites 96.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(\left(z \cdot t\right) \cdot -9, y, 2 \cdot x\right)\right)} \]
7. Add Preprocessing

Alternative 3: 96.3% accurate, N/A× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \mathsf{fma}\left(b \cdot 27, a, \mathsf{fma}\left(y \cdot \left(t \cdot z\right), -9, x \cdot 2\right)\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* b 27.0) a (fma (* y (* t z)) -9.0 (* x 2.0))))

C

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

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(b * 27.0), a, fma(Float64(y * Float64(t * z)), -9.0, Float64(x * 2.0)))
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] * -9.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing
3. 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. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 95.6

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

4. Applied rewrites 95.6%

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

6. Applied rewrites 96.1%

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

   1. lift-*.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. associate-*r* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 96.1

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

8. Applied rewrites 96.1%

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

Alternative 4: 98.3% accurate, N/A× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t\_2 \leq 10^{+121}:\\ \;\;\;\;\left(x \cdot 2 - t\_2 \cdot t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)) (t_2 (* (* y 9.0) z)))
   (if (<= t_2 1e+121)
     (+ (- (* x 2.0) (* t_2 t)) t_1)
     (+ (- (* x 2.0) (* (* t y) (* z 9.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = (y * 9.0) * z;
	double tmp;
	if (t_2 <= 1e+121) {
		tmp = ((x * 2.0) - (t_2 * t)) + t_1;
	} else {
		tmp = ((x * 2.0) - ((t * y) * (z * 9.0))) + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = (y * 9.0d0) * z
    if (t_2 <= 1d+121) then
        tmp = ((x * 2.0d0) - (t_2 * t)) + t_1
    else
        tmp = ((x * 2.0d0) - ((t * y) * (z * 9.0d0))) + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
assert x < y && y < z && z < t && t < a && a < b;
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 = (y * 9.0) * z;
	double tmp;
	if (t_2 <= 1e+121) {
		tmp = ((x * 2.0) - (t_2 * t)) + t_1;
	} else {
		tmp = ((x * 2.0) - ((t * y) * (z * 9.0))) + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = (y * 9.0) * z
	tmp = 0
	if t_2 <= 1e+121:
		tmp = ((x * 2.0) - (t_2 * t)) + t_1
	else:
		tmp = ((x * 2.0) - ((t * y) * (z * 9.0))) + t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(y * 9.0) * z)
	tmp = 0.0
	if (t_2 <= 1e+121)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_2 * t)) + t_1);
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(Float64(t * y) * Float64(z * 9.0))) + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_2 <= 1e+121)
		tmp = ((x * 2.0) - (t_2 * t)) + t_1;
	else
		tmp = ((x * 2.0) - ((t * y) * (z * 9.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$2, 1e+121], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$2 * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y #s(literal 9 binary64)) z) < 1.00000000000000004e121

   1. Initial program 97.2%

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

   if 1.00000000000000004e121 < (*.f64 (*.f64 y #s(literal 9 binary64)) z)

   1. Initial program 83.2%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. Add Preprocessing
   3. 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. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 91.3

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

   4. Applied rewrites 91.3%

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

Alternative 5: 93.2% accurate, N/A× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\\\ [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + \left(a \cdot 27\right) \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* t y) (* z 9.0))) (* (* a 27.0) b)))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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) - ((t * y) * (z * 9.0d0))) + ((a * 27.0d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - ((t * y) * (z * 9.0))) + ((a * 27.0) * b);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.7%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. Add Preprocessing
3. 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. lift-*.f64 N/A

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

   5. associate-*l* N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 95.6

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

4. Applied rewrites 95.6%

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

Reproduce

herbie shell --seed 2025057 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7590524218811189/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b))))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))