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

Percentage Accurate: 95.7% → 98.8%

Time: 3.1s

Alternatives: 15

Speedup: 1.1×

• 27.8% 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: 95.7% 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, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.95 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, -9 \cdot y, \mathsf{fma}\left(a \cdot b, 27, x + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot 27, a, \left(x + x\right) - t \cdot \left(z \cdot \left(9 \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.95e-41)
   (fma (* z t) (* -9.0 y) (fma (* a b) 27.0 (+ x x)))
   (fma (* b 27.0) a (- (+ x x) (* t (* z (* 9.0 y)))))))

C

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 (z <= 1.95e-41) {
		tmp = fma((z * t), (-9.0 * y), fma((a * b), 27.0, (x + x)));
	} else {
		tmp = fma((b * 27.0), a, ((x + x) - (t * (z * (9.0 * y)))));
	}
	return tmp;
}

Julia

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 (z <= 1.95e-41)
		tmp = fma(Float64(z * t), Float64(-9.0 * y), fma(Float64(a * b), 27.0, Float64(x + x)));
	else
		tmp = fma(Float64(b * 27.0), a, Float64(Float64(x + x) - Float64(t * Float64(z * Float64(9.0 * y)))));
	end
	return tmp
end

Wolfram

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[z, 1.95e-41], N[(N[(z * t), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * 27.0), $MachinePrecision] * a + N[(N[(x + x), $MachinePrecision] - N[(t * N[(z * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.94999999999999995e-41

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   7. Applied rewrites 95.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 95.8

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

      9. lift-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-+.f64 N/A

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

      16. count-2-rev N/A

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

      17. lower-fma.f64 N/A

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

      18. count-2-rev N/A

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

      19. lift-+.f64 95.9

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

   9. Applied rewrites 95.9%

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

   if 1.94999999999999995e-41 < z

   1. Initial program 95.7%

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

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 96.3

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. count-2-rev N/A

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

      13. lower-+.f64 96.3

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 96.3

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

      17. lift-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 96.3

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 96.3

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

   3. Applied rewrites 96.3%

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

Alternative 2: 98.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0124:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \mathsf{fma}\left(27 \cdot b, a, x + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + x\right) - \mathsf{fma}\left(t \cdot \left(9 \cdot y\right), z, \left(-27 \cdot a\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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 (<= y -0.0124)
   (fma (* (* t z) -9.0) y (fma (* 27.0 b) a (+ x x)))
   (- (+ x x) (fma (* t (* 9.0 y)) z (* (* -27.0 a) b)))))

C

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 (y <= -0.0124) {
		tmp = fma(((t * z) * -9.0), y, fma((27.0 * b), a, (x + x)));
	} else {
		tmp = (x + x) - fma((t * (9.0 * y)), z, ((-27.0 * a) * b));
	}
	return tmp;
}

Julia

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 (y <= -0.0124)
		tmp = fma(Float64(Float64(t * z) * -9.0), y, fma(Float64(27.0 * b), a, Float64(x + x)));
	else
		tmp = Float64(Float64(x + x) - fma(Float64(t * Float64(9.0 * y)), z, Float64(Float64(-27.0 * a) * b)));
	end
	return tmp
end

Wolfram

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[y, -0.0124], N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + x), $MachinePrecision] - N[(N[(t * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] * z + N[(N[(-27.0 * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0123999999999999996

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   7. Applied rewrites 95.9%

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

   if -0.0123999999999999996 < y

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. count-2-rev N/A

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

      8. lower-+.f64 N/A

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

      9. sub-flip N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*r* N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. distribute-lft-neg-out N/A

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

      21. lower-*.f64 N/A

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

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

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

      25. lower-*.f64 N/A

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

      26. metadata-eval 93.3

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

   3. Applied rewrites 93.3%

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

Alternative 3: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, -9 \cdot y, \mathsf{fma}\left(a \cdot b, 27, x + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1e-45)
   (fma (* z t) (* -9.0 y) (fma (* a b) 27.0 (+ x x)))
   (fma -9.0 (* t (* y z)) (fma 2.0 x (* 27.0 (* a b))))))

C

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 (z <= 1e-45) {
		tmp = fma((z * t), (-9.0 * y), fma((a * b), 27.0, (x + x)));
	} else {
		tmp = fma(-9.0, (t * (y * z)), fma(2.0, x, (27.0 * (a * b))));
	}
	return tmp;
}

Julia

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 (z <= 1e-45)
		tmp = fma(Float64(z * t), Float64(-9.0 * y), fma(Float64(a * b), 27.0, Float64(x + x)));
	else
		tmp = fma(-9.0, Float64(t * Float64(y * z)), fma(2.0, x, Float64(27.0 * Float64(a * b))));
	end
	return tmp
end

Wolfram

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[z, 1e-45], N[(N[(z * t), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.99999999999999984e-46

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   7. Applied rewrites 95.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 95.8

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

      9. lift-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-+.f64 N/A

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

      16. count-2-rev N/A

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

      17. lower-fma.f64 N/A

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

      18. count-2-rev N/A

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

      19. lift-+.f64 95.9

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

   9. Applied rewrites 95.9%

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

   if 9.99999999999999984e-46 < z

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 95.9

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

   4. Applied rewrites 95.9%

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

Alternative 4: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{-61}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot t, -9 \cdot y, \mathsf{fma}\left(a \cdot b, 27, x + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, z \cdot -9, \mathsf{fma}\left(27 \cdot b, a, x + x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2.4e-61)
   (fma (* z t) (* -9.0 y) (fma (* a b) 27.0 (+ x x)))
   (fma (* y t) (* z -9.0) (fma (* 27.0 b) a (+ x x)))))

C

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 (z <= 2.4e-61) {
		tmp = fma((z * t), (-9.0 * y), fma((a * b), 27.0, (x + x)));
	} else {
		tmp = fma((y * t), (z * -9.0), fma((27.0 * b), a, (x + x)));
	}
	return tmp;
}

Julia

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 (z <= 2.4e-61)
		tmp = fma(Float64(z * t), Float64(-9.0 * y), fma(Float64(a * b), 27.0, Float64(x + x)));
	else
		tmp = fma(Float64(y * t), Float64(z * -9.0), fma(Float64(27.0 * b), a, Float64(x + x)));
	end
	return tmp
end

Wolfram

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[z, 2.4e-61], N[(N[(z * t), $MachinePrecision] * N[(-9.0 * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] * 27.0 + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.4000000000000001e-61

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   7. Applied rewrites 95.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 95.8

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

      9. lift-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-+.f64 N/A

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

      16. count-2-rev N/A

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

      17. lower-fma.f64 N/A

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

      18. count-2-rev N/A

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

      19. lift-+.f64 95.9

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

   9. Applied rewrites 95.9%

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

   if 2.4000000000000001e-61 < z

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*r* N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. lift-*.f64 N/A

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

   7. Applied rewrites 93.4%

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

Alternative 5: 98.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(27 \cdot b, a, x + x\right)\\ \mathbf{if}\;z \leq 4 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot z, y \cdot -9, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot t, z \cdot -9, t\_1\right)\\ \end{array} \end{array} \]

FPCore

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 (fma (* 27.0 b) a (+ x x))))
   (if (<= z 4e-65)
     (fma (* t z) (* y -9.0) t_1)
     (fma (* y t) (* z -9.0) t_1))))

C

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 = fma((27.0 * b), a, (x + x));
	double tmp;
	if (z <= 4e-65) {
		tmp = fma((t * z), (y * -9.0), t_1);
	} else {
		tmp = fma((y * t), (z * -9.0), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = fma(Float64(27.0 * b), a, Float64(x + x))
	tmp = 0.0
	if (z <= 4e-65)
		tmp = fma(Float64(t * z), Float64(y * -9.0), t_1);
	else
		tmp = fma(Float64(y * t), Float64(z * -9.0), t_1);
	end
	return tmp
end

Wolfram

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[(27.0 * b), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 4e-65], N[(N[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * N[(z * -9.0), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 3.99999999999999969e-65

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*r* N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. lift-*.f64 N/A

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

   7. Applied rewrites 95.8%

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

   if 3.99999999999999969e-65 < z

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-+r+ N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. associate-*r* N/A

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. associate-*r* N/A

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

      18. *-commutative N/A

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

      19. lift-*.f64 N/A

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

      20. associate-*r* N/A

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

      21. lift-*.f64 N/A

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

   7. Applied rewrites 93.4%

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

Alternative 6: 95.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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((t * z), (y * -9.0), fma((27.0 * b), a, (x + x)));
}

Julia

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

Wolfram

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[(t * z), $MachinePrecision] * N[(y * -9.0), $MachinePrecision] + N[(N[(27.0 * b), $MachinePrecision] * a + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

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

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 95.7

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

3. Applied rewrites 95.7%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. associate-*r* N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 95.7

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 95.7

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

   13. lift--.f64 N/A

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

   14. lift-*.f64 N/A

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

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

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

   16. lift-*.f64 N/A

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

   17. *-commutative N/A

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

   18. lower-fma.f64 N/A

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

   19. metadata-eval N/A

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

   20. lower-*.f64 95.7

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

   21. lift-*.f64 N/A

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

   22. *-commutative N/A

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

   23. lower-*.f64 95.7

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

   24. lift-*.f64 N/A

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

   25. *-commutative N/A

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

   26. lower-*.f64 95.7

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

5. Applied rewrites 95.7%

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

   1. lift-fma.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. associate-+r+ N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. lift-*.f64 N/A

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

   9. +-commutative N/A

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

   10. lift-fma.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. associate-*r* N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. associate-*r* N/A

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

   17. associate-*r* N/A

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

   18. *-commutative N/A

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

   19. lift-*.f64 N/A

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

   20. associate-*r* N/A

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

   21. lift-*.f64 N/A

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

7. Applied rewrites 95.8%

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

Alternative 7: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := \mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, t\_1\right)\\ t_3 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(2, x, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

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 (* 27.0 (* a b)))
        (t_2 (fma (* (* t z) -9.0) y t_1))
        (t_3 (* (* (* y 9.0) z) t)))
   (if (<= t_3 -5e+172) t_2 (if (<= t_3 2e+117) (fma 2.0 x t_1) t_2))))

C

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 = 27.0 * (a * b);
	double t_2 = fma(((t * z) * -9.0), y, t_1);
	double t_3 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_3 <= -5e+172) {
		tmp = t_2;
	} else if (t_3 <= 2e+117) {
		tmp = fma(2.0, x, t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = fma(Float64(Float64(t * z) * -9.0), y, t_1)
	t_3 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_3 <= -5e+172)
		tmp = t_2;
	elseif (t_3 <= 2e+117)
		tmp = fma(2.0, x, t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * z), $MachinePrecision] * -9.0), $MachinePrecision] * y + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+172], t$95$2, If[LessEqual[t$95$3, 2e+117], N[(2.0 * x + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e172 or 2.0000000000000001e117 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   7. Applied rewrites 95.9%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 66.8

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

   10. Applied rewrites 66.8%

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

   if -5.0000000000000001e172 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e117

   1. Initial program 95.7%

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

   2. 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-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

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

Alternative 8: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1.56 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(-9, \left(t \cdot y\right) \cdot z, t\_1\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(2, x, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), t\_1\right)\\ \end{array} \end{array} \]

FPCore

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 (* 27.0 (* a b))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -1.56e+82)
     (fma -9.0 (* (* t y) z) t_1)
     (if (<= t_2 2e+117) (fma 2.0 x t_1) (fma -9.0 (* t (* y z)) t_1)))))

C

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 = 27.0 * (a * b);
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1.56e+82) {
		tmp = fma(-9.0, ((t * y) * z), t_1);
	} else if (t_2 <= 2e+117) {
		tmp = fma(2.0, x, t_1);
	} else {
		tmp = fma(-9.0, (t * (y * z)), t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -1.56e+82)
		tmp = fma(-9.0, Float64(Float64(t * y) * z), t_1);
	elseif (t_2 <= 2e+117)
		tmp = fma(2.0, x, t_1);
	else
		tmp = fma(-9.0, Float64(t * Float64(y * z)), t_1);
	end
	return tmp
end

Wolfram

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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1.56e+82], N[(-9.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+117], N[(2.0 * x + t$95$1), $MachinePrecision], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.56e82

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 66.6

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

   8. Applied rewrites 66.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 64.4

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

   10. Applied rewrites 64.4%

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

   if -1.56e82 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e117

   1. Initial program 95.7%

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

   2. 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-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

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

   if 2.0000000000000001e117 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 66.6

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

   8. Applied rewrites 66.6%

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

Alternative 9: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := \mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), t\_1\right)\\ t_3 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_3 \leq -1.56 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(2, x, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

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 (* 27.0 (* a b)))
        (t_2 (fma -9.0 (* t (* y z)) t_1))
        (t_3 (* (* (* y 9.0) z) t)))
   (if (<= t_3 -1.56e+82) t_2 (if (<= t_3 2e+117) (fma 2.0 x t_1) t_2))))

C

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 = 27.0 * (a * b);
	double t_2 = fma(-9.0, (t * (y * z)), t_1);
	double t_3 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_3 <= -1.56e+82) {
		tmp = t_2;
	} else if (t_3 <= 2e+117) {
		tmp = fma(2.0, x, t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(27.0 * Float64(a * b))
	t_2 = fma(-9.0, Float64(t * Float64(y * z)), t_1)
	t_3 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_3 <= -1.56e+82)
		tmp = t_2;
	elseif (t_3 <= 2e+117)
		tmp = fma(2.0, x, t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$3, -1.56e+82], t$95$2, If[LessEqual[t$95$3, 2e+117], N[(2.0 * x + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.56e82 or 2.0000000000000001e117 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 66.6

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

   8. Applied rewrites 66.6%

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

   if -1.56e82 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e117

   1. Initial program 95.7%

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

   2. 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-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

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

Alternative 10: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(27 \cdot a, b, x + x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(-9, t \cdot \left(y \cdot z\right), 2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b)))
   (if (<= t_1 -2e+33)
     (fma (* 27.0 a) b (+ x x))
     (if (<= t_1 2e+66)
       (fma -9.0 (* t (* y z)) (* 2.0 x))
       (fma 2.0 x (* 27.0 (* a b)))))))

C

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 tmp;
	if (t_1 <= -2e+33) {
		tmp = fma((27.0 * a), b, (x + x));
	} else if (t_1 <= 2e+66) {
		tmp = fma(-9.0, (t * (y * z)), (2.0 * x));
	} else {
		tmp = fma(2.0, x, (27.0 * (a * b)));
	}
	return tmp;
}

Julia

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)
	tmp = 0.0
	if (t_1 <= -2e+33)
		tmp = fma(Float64(27.0 * a), b, Float64(x + x));
	elseif (t_1 <= 2e+66)
		tmp = fma(-9.0, Float64(t * Float64(y * z)), Float64(2.0 * x));
	else
		tmp = fma(2.0, x, Float64(27.0 * Float64(a * b)));
	end
	return tmp
end

Wolfram

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]}, If[LessEqual[t$95$1, -2e+33], N[(N[(27.0 * a), $MachinePrecision] * b + N[(x + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+66], N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], N[(2.0 * x + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -1.9999999999999999e33

   1. Initial program 95.7%

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

   2. 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-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 65.1

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

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a \cdot 27, b, x \cdot 2\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, x \cdot 2\right) \]

      13. lower-*.f64 65.1

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, x \cdot 2\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, x \cdot 2\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, 2 \cdot x\right) \]

      16. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, x + x\right) \]

      17. lift-+.f64 65.1

          \[\leadsto \mathsf{fma}\left(27 \cdot a, b, x + x\right) \]

   6. Applied rewrites 65.1%

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

   if -1.9999999999999999e33 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.99999999999999989e66

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 95.7

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 95.7

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

      13. lift--.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval N/A

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

      20. lower-*.f64 95.7

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

      21. lift-*.f64 N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 95.7

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 95.7

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

   5. Applied rewrites 95.7%

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

   7. Applied rewrites 95.9%

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

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right) + 2 \cdot x} \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 64.4

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

   10. Applied rewrites 64.4%

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

   if 1.99999999999999989e66 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.7%

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

   2. 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-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

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

Alternative 11: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -5e+172)
     t_1
     (if (<= t_2 4e+163) (fma 2.0 x (* 27.0 (* a b))) t_1))))

C

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 = -9.0 * (t * (y * z));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -5e+172) {
		tmp = t_1;
	} else if (t_2 <= 4e+163) {
		tmp = fma(2.0, x, (27.0 * (a * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -5e+172)
		tmp = t_1;
	elseif (t_2 <= 4e+163)
		tmp = fma(2.0, x, Float64(27.0 * Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

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[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+172], t$95$1, If[LessEqual[t$95$2, 4e+163], N[(2.0 * x + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e172 or 3.9999999999999998e163 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.7%

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

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

      3. associate-*l* N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 95.7

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

   3. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      9. lower-fma.f64 95.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot b, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot b}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      12. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      15. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{2 \cdot x} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{\mathsf{fma}\left(2, x, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) \]

      20. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      21. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      23. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      24. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(t \cdot z\right)} \cdot y\right)\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

      26. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

   5. Applied rewrites 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\left(z \cdot t\right) \cdot y\right)\right)\right)} \]

   7. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \mathsf{fma}\left(27 \cdot b, a, x + x\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      3. lower-*.f64 35.6

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

   10. Applied rewrites 35.6%

       \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if -5.0000000000000001e172 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 3.9999999999999998e163

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. 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-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -5e+172)
     t_1
     (if (<= t_2 4e+163) (fma a (* 27.0 b) (+ x x)) t_1))))

C

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 = -9.0 * (t * (y * z));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -5e+172) {
		tmp = t_1;
	} else if (t_2 <= 4e+163) {
		tmp = fma(a, (27.0 * b), (x + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -5e+172)
		tmp = t_1;
	elseif (t_2 <= 4e+163)
		tmp = fma(a, Float64(27.0 * b), Float64(x + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

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[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+172], t$95$1, If[LessEqual[t$95$2, 4e+163], N[(a * N[(27.0 * b), $MachinePrecision] + N[(x + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -5.0000000000000001e172 or 3.9999999999999998e163 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      5. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      6. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      9. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

      10. lower-*.f64 95.7

          \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   3. Applied rewrites 95.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      9. lower-fma.f64 95.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot b, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot b}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      12. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      15. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{2 \cdot x} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{\mathsf{fma}\left(2, x, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) \]

      20. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      21. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      23. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      24. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(t \cdot z\right)} \cdot y\right)\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

      26. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

   5. Applied rewrites 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\left(z \cdot t\right) \cdot y\right)\right)\right)} \]

   7. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \mathsf{fma}\left(27 \cdot b, a, x + x\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      3. lower-*.f64 35.6

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

   10. Applied rewrites 35.6%

       \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if -5.0000000000000001e172 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 3.9999999999999998e163

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. 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-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto 2 \cdot x + \color{blue}{27 \cdot \left(a \cdot b\right)} \]

      2. *-commutative N/A

         \[\leadsto x \cdot 2 + \color{blue}{27} \cdot \left(a \cdot b\right) \]

      3. lift-*.f64 N/A

         \[\leadsto x \cdot 2 + \color{blue}{27} \cdot \left(a \cdot b\right) \]

      4. +-commutative N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{x \cdot 2} \]

      5. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + \color{blue}{x} \cdot 2 \]

      6. lift-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot b\right) + x \cdot 2 \]

      7. associate-*r* N/A

         \[\leadsto \left(27 \cdot a\right) \cdot b + \color{blue}{x} \cdot 2 \]

      8. *-commutative N/A

         \[\leadsto \left(a \cdot 27\right) \cdot b + x \cdot 2 \]

      9. associate-*l* N/A

         \[\leadsto a \cdot \left(27 \cdot b\right) + \color{blue}{x} \cdot 2 \]

      10. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x \cdot 2\right) \]

      11. lower-*.f64 65.1

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot \color{blue}{b}, x \cdot 2\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, 2 \cdot x\right) \]

      14. count-2-rev N/A

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x + x\right) \]

      15. lift-+.f64 65.1

          \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x + x\right) \]

   6. Applied rewrites 65.1%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{27 \cdot b}, x + x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 55.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := -9 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ \mathbf{if}\;t\_2 \leq -1.56 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+117}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -9.0 (* t (* y z)))) (t_2 (* (* (* y 9.0) z) t)))
   (if (<= t_2 -1.56e+82) t_1 (if (<= t_2 2e+117) (+ x x) t_1))))

C

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 = -9.0 * (t * (y * z));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1.56e+82) {
		tmp = t_1;
	} else if (t_2 <= 2e+117) {
		tmp = x + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = (-9.0d0) * (t * (y * z))
    t_2 = ((y * 9.0d0) * z) * t
    if (t_2 <= (-1.56d+82)) then
        tmp = t_1
    else if (t_2 <= 2d+117) then
        tmp = x + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 = -9.0 * (t * (y * z));
	double t_2 = ((y * 9.0) * z) * t;
	double tmp;
	if (t_2 <= -1.56e+82) {
		tmp = t_1;
	} else if (t_2 <= 2e+117) {
		tmp = x + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = -9.0 * (t * (y * z))
	t_2 = ((y * 9.0) * z) * t
	tmp = 0
	if t_2 <= -1.56e+82:
		tmp = t_1
	elif t_2 <= 2e+117:
		tmp = x + x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(-9.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(Float64(Float64(y * 9.0) * z) * t)
	tmp = 0.0
	if (t_2 <= -1.56e+82)
		tmp = t_1;
	elseif (t_2 <= 2e+117)
		tmp = Float64(x + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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 = -9.0 * (t * (y * z));
	t_2 = ((y * 9.0) * z) * t;
	tmp = 0.0;
	if (t_2 <= -1.56e+82)
		tmp = t_1;
	elseif (t_2 <= 2e+117)
		tmp = x + x;
	else
		tmp = 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.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-9.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1.56e+82], t$95$1, If[LessEqual[t$95$2, 2e+117], N[(x + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < -1.56e82 or 2.0000000000000001e117 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t)

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      5. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      6. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      9. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

      10. lower-*.f64 95.7

          \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   3. Applied rewrites 95.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      9. lower-fma.f64 95.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot b, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot b}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      12. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      15. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{2 \cdot x} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{\mathsf{fma}\left(2, x, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) \]

      20. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      21. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      23. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      24. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(t \cdot z\right)} \cdot y\right)\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

      26. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

   5. Applied rewrites 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\left(z \cdot t\right) \cdot y\right)\right)\right)} \]

   7. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(t \cdot z\right) \cdot -9, y, \mathsf{fma}\left(27 \cdot b, a, x + x\right)\right)} \]

   8. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -9 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \]

      3. lower-*.f64 35.6

         \[\leadsto -9 \cdot \left(t \cdot \left(y \cdot \color{blue}{z}\right)\right) \]

   10. Applied rewrites 35.6%

       \[\leadsto \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} \]

   if -1.56e82 < (*.f64 (*.f64 (*.f64 y #s(literal 9 binary64)) z) t) < 2.0000000000000001e117

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      5. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      6. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      9. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

      10. lower-*.f64 95.7

          \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   3. Applied rewrites 95.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      9. lower-fma.f64 95.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot b, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot b}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      12. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      15. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{2 \cdot x} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{\mathsf{fma}\left(2, x, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) \]

      20. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      21. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      23. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      24. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(t \cdot z\right)} \cdot y\right)\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

      26. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

   5. Applied rewrites 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\left(z \cdot t\right) \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   7. Step-by-step derivation

      1. lower-*.f64 31.3

         \[\leadsto 2 \cdot \color{blue}{x} \]

   8. Applied rewrites 31.3%

      \[\leadsto \color{blue}{2 \cdot x} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{x} \]

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lift-+.f64 31.3

         \[\leadsto x + \color{blue}{x} \]

   10. Applied rewrites 31.3%

       \[\leadsto \color{blue}{x + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+139}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

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 (* 27.0 (* a b))))
   (if (<= t_1 -4e+172) t_2 (if (<= t_1 1e+139) (+ x x) t_2))))

C

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 = 27.0 * (a * b);
	double tmp;
	if (t_1 <= -4e+172) {
		tmp = t_2;
	} else if (t_1 <= 1e+139) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 = 27.0d0 * (a * b)
    if (t_1 <= (-4d+172)) then
        tmp = t_2
    else if (t_1 <= 1d+139) then
        tmp = x + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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 = 27.0 * (a * b);
	double tmp;
	if (t_1 <= -4e+172) {
		tmp = t_2;
	} else if (t_1 <= 1e+139) {
		tmp = x + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[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 = 27.0 * (a * b)
	tmp = 0
	if t_1 <= -4e+172:
		tmp = t_2
	elif t_1 <= 1e+139:
		tmp = x + x
	else:
		tmp = t_2
	return tmp

Julia

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(27.0 * Float64(a * b))
	tmp = 0.0
	if (t_1 <= -4e+172)
		tmp = t_2;
	elseif (t_1 <= 1e+139)
		tmp = Float64(x + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

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 = 27.0 * (a * b);
	tmp = 0.0;
	if (t_1 <= -4e+172)
		tmp = t_2;
	elseif (t_1 <= 1e+139)
		tmp = x + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+172], t$95$2, If[LessEqual[t$95$1, 1e+139], N[(x + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 a #s(literal 27 binary64)) b) < -4.0000000000000003e172 or 1.00000000000000003e139 < (*.f64 (*.f64 a #s(literal 27 binary64)) b)

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. 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-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, \color{blue}{x}, 27 \cdot \left(a \cdot b\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

      3. lower-*.f64 65.2

         \[\leadsto \mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right) \]

   4. Applied rewrites 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 27 \cdot \left(a \cdot \color{blue}{b}\right) \]

      2. lower-*.f64 35.8

         \[\leadsto 27 \cdot \left(a \cdot b\right) \]

   7. Applied rewrites 35.8%

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} \]

   if -4.0000000000000003e172 < (*.f64 (*.f64 a #s(literal 27 binary64)) b) < 1.00000000000000003e139

   1. Initial program 95.7%

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
   2. 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. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

      3. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      4. lift-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      5. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

      6. associate-*l* N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      7. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      8. lower-*.f64 N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

      9. *-commutative N/A

         \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

      10. lower-*.f64 95.7

          \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   3. Applied rewrites 95.7%

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
   4. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      9. lower-fma.f64 95.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot b, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot b}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      12. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      14. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      15. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

      16. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{2 \cdot x} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{\mathsf{fma}\left(2, x, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) \]

      20. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      21. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      22. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      23. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

      24. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(t \cdot z\right)} \cdot y\right)\right)\right) \]

      25. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

      26. lower-*.f64 95.7

          \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

   5. Applied rewrites 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\left(z \cdot t\right) \cdot y\right)\right)\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot x} \]
   7. Step-by-step derivation

      1. lower-*.f64 31.3

         \[\leadsto 2 \cdot \color{blue}{x} \]

   8. Applied rewrites 31.3%

      \[\leadsto \color{blue}{2 \cdot x} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 2 \cdot \color{blue}{x} \]

      2. count-2-rev N/A

         \[\leadsto x + \color{blue}{x} \]

      3. lift-+.f64 31.3

         \[\leadsto x + \color{blue}{x} \]

   10. Applied rewrites 31.3%

       \[\leadsto \color{blue}{x + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 31.3% accurate, 6.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x + x \end{array} \]

FPCore

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 x))

C

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 + x;
}

Fortran

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 + x
end function

Java

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 + x;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x + x

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(x + x)
end

MATLAB

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 + x;
end

Wolfram

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[(x + x), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
2. 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. lift-*.f64 N/A

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(\left(y \cdot 9\right) \cdot z\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   3. associate-*l* N/A

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   4. lift-*.f64 N/A

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

   5. *-commutative N/A

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b \]

   6. associate-*l* N/A

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   7. lower-*.f64 N/A

      \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   8. lower-*.f64 N/A

      \[\leadsto \left(x \cdot 2 - 9 \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   9. *-commutative N/A

      \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

   10. lower-*.f64 95.7

       \[\leadsto \left(x \cdot 2 - 9 \cdot \left(y \cdot \color{blue}{\left(t \cdot z\right)}\right)\right) + \left(a \cdot 27\right) \cdot b \]

3. Applied rewrites 95.7%

   \[\leadsto \left(x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
4. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(a \cdot 27\right) \cdot b} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(a \cdot 27\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   5. *-commutative N/A

      \[\leadsto \color{blue}{\left(27 \cdot a\right)} \cdot b + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   6. associate-*r* N/A

      \[\leadsto \color{blue}{27 \cdot \left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   7. lift-*.f64 N/A

      \[\leadsto 27 \cdot \color{blue}{\left(a \cdot b\right)} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   8. *-commutative N/A

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot 27} + \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   9. lower-fma.f64 95.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot b, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]

   10. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{a \cdot b}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   11. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   12. lower-*.f64 95.7

       \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot a}, 27, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   13. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

   14. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

   15. fp-cancel-sub-sign-inv N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2 + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right) \]

   16. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{x \cdot 2} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   17. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{2 \cdot x} + \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]

   18. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \color{blue}{\mathsf{fma}\left(2, x, \left(\mathsf{neg}\left(9\right)\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9} \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) \]

   20. lower-*.f64 95.7

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, \color{blue}{-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

   21. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right)\right) \]

   22. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

   23. lower-*.f64 95.7

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right)\right) \]

   24. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(t \cdot z\right)} \cdot y\right)\right)\right) \]

   25. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

   26. lower-*.f64 95.7

       \[\leadsto \mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\color{blue}{\left(z \cdot t\right)} \cdot y\right)\right)\right) \]

5. Applied rewrites 95.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot a, 27, \mathsf{fma}\left(2, x, -9 \cdot \left(\left(z \cdot t\right) \cdot y\right)\right)\right)} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{2 \cdot x} \]
7. Step-by-step derivation

   1. lower-*.f64 31.3

      \[\leadsto 2 \cdot \color{blue}{x} \]

8. Applied rewrites 31.3%

   \[\leadsto \color{blue}{2 \cdot x} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto 2 \cdot \color{blue}{x} \]

   2. count-2-rev N/A

      \[\leadsto x + \color{blue}{x} \]

   3. lift-+.f64 31.3

      \[\leadsto x + \color{blue}{x} \]

10. Applied rewrites 31.3%

    \[\leadsto \color{blue}{x + x} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025156 
(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)))