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

Percentage Accurate: 85.3% → 92.1%

Time: 7.1s

Alternatives: 20

Speedup: 1.0×

• 50.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

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, c, i, j, k)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

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, c, i, j, k)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(-x \cdot \left(i \cdot 4 - \left(\left(y \cdot 18\right) \cdot t\right) \cdot z\right)\right) + \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -8 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+
           (- (* x (- (* i 4.0) (* (* (* y 18.0) t) z))))
           (fma (* a t) -4.0 (* c b)))
          (* (* j 27.0) k))))
   (if (<= x -8e-47)
     t_1
     (if (<= x 1.65e+177)
       (fma
        (* -27.0 k)
        j
        (fma (* i x) -4.0 (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (* c b))))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-(x * ((i * 4.0) - (((y * 18.0) * t) * z))) + fma((a * t), -4.0, (c * b))) - ((j * 27.0) * k);
	double tmp;
	if (x <= -8e-47) {
		tmp = t_1;
	} else if (x <= 1.65e+177) {
		tmp = fma((-27.0 * k), j, fma((i * x), -4.0, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, (c * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(-Float64(x * Float64(Float64(i * 4.0) - Float64(Float64(Float64(y * 18.0) * t) * z)))) + fma(Float64(a * t), -4.0, Float64(c * b))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (x <= -8e-47)
		tmp = t_1;
	elseif (x <= 1.65e+177)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(i * x), -4.0, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, Float64(c * b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[((-N[(x * N[(N[(i * 4.0), $MachinePrecision] - N[(N[(N[(y * 18.0), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e-47], t$95$1, If[LessEqual[x, 1.65e+177], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.9999999999999998e-47 or 1.6500000000000001e177 < x

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 87.4%

      \[\leadsto \color{blue}{\left(\left(-x \cdot \left(i \cdot 4 - \left(\left(y \cdot 18\right) \cdot t\right) \cdot z\right)\right) + \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -7.9999999999999998e-47 < x < 1.6500000000000001e177

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.35e+185)
   (* x (fma -4.0 i (* 18.0 (* t (* y z)))))
   (fma
    (* -27.0 k)
    j
    (fma (* i x) -4.0 (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.35e+185) {
		tmp = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	} else {
		tmp = fma((-27.0 * k), j, fma((i * x), -4.0, fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, (c * b))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.35e+185)
		tmp = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))));
	else
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(i * x), -4.0, fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, Float64(c * b))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.35e+185], N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000003e185

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, \color{blue}{i}, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.6

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.6%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.35000000000000003e185 < x

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y \cdot t, \left(18 \cdot x\right) \cdot z, \mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(-4 \cdot x, i, b \cdot c\right)\right)\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+248}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 61000000:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* y t)
          (* (* 18.0 x) z)
          (fma (* j k) -27.0 (fma (* -4.0 x) i (* b c))))))
   (if (<= y -3e+248)
     (* t (fma -4.0 a (* 18.0 (* x (* y z)))))
     (if (<= y -7.2e+49)
       t_1
       (if (<= y 61000000.0)
         (fma (* -27.0 k) j (fma (* i x) -4.0 (fma (* -4.0 a) t (* c b))))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((y * t), ((18.0 * x) * z), fma((j * k), -27.0, fma((-4.0 * x), i, (b * c))));
	double tmp;
	if (y <= -3e+248) {
		tmp = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	} else if (y <= -7.2e+49) {
		tmp = t_1;
	} else if (y <= 61000000.0) {
		tmp = fma((-27.0 * k), j, fma((i * x), -4.0, fma((-4.0 * a), t, (c * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(y * t), Float64(Float64(18.0 * x) * z), fma(Float64(j * k), -27.0, fma(Float64(-4.0 * x), i, Float64(b * c))))
	tmp = 0.0
	if (y <= -3e+248)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))));
	elseif (y <= -7.2e+49)
		tmp = t_1;
	elseif (y <= 61000000.0)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(i * x), -4.0, fma(Float64(-4.0 * a), t, Float64(c * b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(y * t), $MachinePrecision] * N[(N[(18.0 * x), $MachinePrecision] * z), $MachinePrecision] + N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(-4.0 * x), $MachinePrecision] * i + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+248], N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e+49], t$95$1, If[LessEqual[y, 61000000.0], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e248

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -3e248 < y < -7.19999999999999993e49 or 6.1e7 < y

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \color{blue}{\left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot \color{blue}{x}\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      10. lower-*.f64 71.6

          \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   6. Applied rewrites 73.3%

      \[\leadsto \mathsf{fma}\left(y \cdot t, \color{blue}{\left(18 \cdot x\right) \cdot z}, \mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(-4 \cdot x, i, b \cdot c\right)\right)\right) \]

   if -7.19999999999999993e49 < y < 6.1e7

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, c \cdot b\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 78.6

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-4 \cdot \color{blue}{a}, t, c \cdot b\right)\right)\right) \]

   6. Applied rewrites 78.6%

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

Alternative 4: 79.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, -4 \cdot \left(a \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -9e+142)
   (fma (* -27.0 k) j (fma (* (* t (* 18.0 x)) z) y (* -4.0 (* a t))))
   (if (<= y 1.35e+184)
     (fma (* -27.0 k) j (fma (* i x) -4.0 (fma (* -4.0 a) t (* c b))))
     (- (fma 18.0 (* t (* x (* y z))) (* b c)) (* 4.0 (* i x))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (y <= -9e+142) {
		tmp = fma((-27.0 * k), j, fma(((t * (18.0 * x)) * z), y, (-4.0 * (a * t))));
	} else if (y <= 1.35e+184) {
		tmp = fma((-27.0 * k), j, fma((i * x), -4.0, fma((-4.0 * a), t, (c * b))));
	} else {
		tmp = fma(18.0, (t * (x * (y * z))), (b * c)) - (4.0 * (i * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -9e+142)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(Float64(t * Float64(18.0 * x)) * z), y, Float64(-4.0 * Float64(a * t))));
	elseif (y <= 1.35e+184)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(i * x), -4.0, fma(Float64(-4.0 * a), t, Float64(c * b))));
	else
		tmp = Float64(fma(18.0, Float64(t * Float64(x * Float64(y * z))), Float64(b * c)) - Float64(4.0 * Float64(i * x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -9e+142], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(N[(t * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * y + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+184], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999998e142

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   5. Applied rewrites 88.2%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, \mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(-4 \cdot x, i, b \cdot c\right)\right)\right)}\right) \]

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      2. lower-*.f64 58.8

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, -4 \cdot \left(a \cdot \color{blue}{t}\right)\right)\right) \]

   8. Applied rewrites 58.8%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, \color{blue}{-4 \cdot \left(a \cdot t\right)}\right)\right) \]

   if -8.9999999999999998e142 < y < 1.35e184

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, c \cdot b\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 78.6

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-4 \cdot \color{blue}{a}, t, c \cdot b\right)\right)\right) \]

   6. Applied rewrites 78.6%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, c \cdot b\right)\right)\right) \]

   if 1.35e184 < y

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \color{blue}{\left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot \color{blue}{x}\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      10. lower-*.f64 71.6

          \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 55.1

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 55.1%

      \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 78.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4, a, 18 \cdot t\_1\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+184}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18, t \cdot t\_1, b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -2.1e+249)
     (* t (fma -4.0 a (* 18.0 t_1)))
     (if (<= y 1.35e+184)
       (fma (* -27.0 k) j (fma (* i x) -4.0 (fma (* -4.0 a) t (* c b))))
       (- (fma 18.0 (* t t_1) (* b c)) (* 4.0 (* i x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -2.1e+249) {
		tmp = t * fma(-4.0, a, (18.0 * t_1));
	} else if (y <= 1.35e+184) {
		tmp = fma((-27.0 * k), j, fma((i * x), -4.0, fma((-4.0 * a), t, (c * b))));
	} else {
		tmp = fma(18.0, (t * t_1), (b * c)) - (4.0 * (i * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -2.1e+249)
		tmp = Float64(t * fma(-4.0, a, Float64(18.0 * t_1)));
	elseif (y <= 1.35e+184)
		tmp = fma(Float64(-27.0 * k), j, fma(Float64(i * x), -4.0, fma(Float64(-4.0 * a), t, Float64(c * b))));
	else
		tmp = Float64(fma(18.0, Float64(t * t_1), Float64(b * c)) - Float64(4.0 * Float64(i * x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+249], N[(t * N[(-4.0 * a + N[(18.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+184], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(18.0 * N[(t * t$95$1), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0999999999999998e249

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -2.0999999999999998e249 < y < 1.35e184

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, c \cdot b\right)\right)\right) \]
   5. Step-by-step derivation

      1. lower-*.f64 78.6

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-4 \cdot \color{blue}{a}, t, c \cdot b\right)\right)\right) \]

   6. Applied rewrites 78.6%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\color{blue}{-4 \cdot a}, t, c \cdot b\right)\right)\right) \]

   if 1.35e184 < y

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \color{blue}{\left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot \color{blue}{x}\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      10. lower-*.f64 71.6

          \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 55.1

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 55.1%

      \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* 18.0 (* t (* y z)))))))
   (if (<= x -5.2e+192)
     t_1
     (if (<= x -5.4e-16)
       (- (fma 18.0 (* t (* x (* y z))) (* b c)) (* 4.0 (* i x)))
       (if (<= x 1.2e+111)
         (fma (* -27.0 k) j (fma -4.0 (* a t) (* b c)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -5.2e+192) {
		tmp = t_1;
	} else if (x <= -5.4e-16) {
		tmp = fma(18.0, (t * (x * (y * z))), (b * c)) - (4.0 * (i * x));
	} else if (x <= 1.2e+111) {
		tmp = fma((-27.0 * k), j, fma(-4.0, (a * t), (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -5.2e+192)
		tmp = t_1;
	elseif (x <= -5.4e-16)
		tmp = Float64(fma(18.0, Float64(t * Float64(x * Float64(y * z))), Float64(b * c)) - Float64(4.0 * Float64(i * x)));
	elseif (x <= 1.2e+111)
		tmp = fma(Float64(-27.0 * k), j, fma(-4.0, Float64(a * t), Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e+192], t$95$1, If[LessEqual[x, -5.4e-16], N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+111], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.20000000000000006e192 or 1.20000000000000003e111 < x

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, \color{blue}{i}, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.6

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.6%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   if -5.20000000000000006e192 < x < -5.39999999999999999e-16

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \color{blue}{\left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot \color{blue}{x}\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      10. lower-*.f64 71.6

          \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 55.1

         \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 55.1%

      \[\leadsto \mathsf{fma}\left(18, t \cdot \left(x \cdot \left(y \cdot z\right)\right), b \cdot c\right) - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]

   if -5.39999999999999999e-16 < x < 1.20000000000000003e111

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c}\right) \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, b \cdot c\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot \color{blue}{t}, b \cdot c\right)\right) \]

      3. lower-*.f64 62.0

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right) \]

   6. Applied rewrites 62.0%

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

Alternative 7: 73.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;b \cdot c - \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.08e+142)
     t_1
     (if (<= t -2.8e-37)
       (- (* b c) (fma 4.0 (* a t) (* 27.0 (* j k))))
       (if (<= t 4e+114)
         (fma (* i -4.0) x (fma b c (* (* j k) -27.0)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.08e+142) {
		tmp = t_1;
	} else if (t <= -2.8e-37) {
		tmp = (b * c) - fma(4.0, (a * t), (27.0 * (j * k)));
	} else if (t <= 4e+114) {
		tmp = fma((i * -4.0), x, fma(b, c, ((j * k) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.08e+142)
		tmp = t_1;
	elseif (t <= -2.8e-37)
		tmp = Float64(Float64(b * c) - fma(4.0, Float64(a * t), Float64(27.0 * Float64(j * k))));
	elseif (t <= 4e+114)
		tmp = fma(Float64(i * -4.0), x, fma(b, c, Float64(Float64(j * k) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.08e+142], t$95$1, If[LessEqual[t, -2.8e-37], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(a * t), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+114], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08e142 or 4e114 < t

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.08e142 < t < -2.8000000000000001e-37

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(a \cdot t\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{a \cdot t}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, a \cdot \color{blue}{t}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.4

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.4%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, a \cdot t, 27 \cdot \left(j \cdot k\right)\right)} \]

   if -2.8000000000000001e-37 < t < 4e114

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

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

Alternative 8: 73.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.08e+142)
     t_1
     (if (<= t -2.9e-38)
       (fma (* -27.0 k) j (fma -4.0 (* a t) (* b c)))
       (if (<= t 4e+114)
         (fma (* i -4.0) x (fma b c (* (* j k) -27.0)))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.08e+142) {
		tmp = t_1;
	} else if (t <= -2.9e-38) {
		tmp = fma((-27.0 * k), j, fma(-4.0, (a * t), (b * c)));
	} else if (t <= 4e+114) {
		tmp = fma((i * -4.0), x, fma(b, c, ((j * k) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.08e+142)
		tmp = t_1;
	elseif (t <= -2.9e-38)
		tmp = fma(Float64(-27.0 * k), j, fma(-4.0, Float64(a * t), Float64(b * c)));
	elseif (t <= 4e+114)
		tmp = fma(Float64(i * -4.0), x, fma(b, c, Float64(Float64(j * k) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.08e+142], t$95$1, If[LessEqual[t, -2.9e-38], N[(N[(-27.0 * k), $MachinePrecision] * j + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+114], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08e142 or 4e114 < t

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.08e142 < t < -2.89999999999999994e-38

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c}\right) \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, b \cdot c\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot \color{blue}{t}, b \cdot c\right)\right) \]

      3. lower-*.f64 62.0

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right) \]

   6. Applied rewrites 62.0%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)}\right) \]

   if -2.89999999999999994e-38 < t < 4e114

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

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

Alternative 9: 73.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -2.9e+142)
     t_1
     (if (<= t 4e+114) (fma (* i -4.0) x (fma b c (* (* j k) -27.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -2.9e+142) {
		tmp = t_1;
	} else if (t <= 4e+114) {
		tmp = fma((i * -4.0), x, fma(b, c, ((j * k) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -2.9e+142)
		tmp = t_1;
	elseif (t <= 4e+114)
		tmp = fma(Float64(i * -4.0), x, fma(b, c, Float64(Float64(j * k) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+142], t$95$1, If[LessEqual[t, 4e+114], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000013e142 or 4e114 < t

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -2.90000000000000013e142 < t < 4e114

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

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

Alternative 10: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-144}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-275}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-169}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.35e+61)
     t_1
     (if (<= t -1.02e-144)
       (fma c b (- (* (* j k) 27.0)))
       (if (<= t -5e-275)
         (- (* b c) (* 4.0 (* i x)))
         (if (<= t 2.1e-169)
           (fma (* i -4.0) x (* -27.0 (* j k)))
           (if (<= t 1.6e+114) (fma -27.0 (* j k) (* b c)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.35e+61) {
		tmp = t_1;
	} else if (t <= -1.02e-144) {
		tmp = fma(c, b, -((j * k) * 27.0));
	} else if (t <= -5e-275) {
		tmp = (b * c) - (4.0 * (i * x));
	} else if (t <= 2.1e-169) {
		tmp = fma((i * -4.0), x, (-27.0 * (j * k)));
	} else if (t <= 1.6e+114) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.35e+61)
		tmp = t_1;
	elseif (t <= -1.02e-144)
		tmp = fma(c, b, Float64(-Float64(Float64(j * k) * 27.0)));
	elseif (t <= -5e-275)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	elseif (t <= 2.1e-169)
		tmp = fma(Float64(i * -4.0), x, Float64(-27.0 * Float64(j * k)));
	elseif (t <= 1.6e+114)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+61], t$95$1, If[LessEqual[t, -1.02e-144], N[(c * b + (-N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, -5e-275], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-169], N[(N[(i * -4.0), $MachinePrecision] * x + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+114], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.3500000000000001e61 or 1.6e114 < t

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.3500000000000001e61 < t < -1.01999999999999997e-144

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      2. lower-*.f64 43.8

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 43.8%

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      2. sub-flip N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, \mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) \]

      6. lower-neg.f64 44.2

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right) \]

      9. lower-*.f64 44.2

         \[\leadsto \mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right) \]

   9. Applied rewrites 44.2%

      \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, -\left(j \cdot k\right) \cdot 27\right) \]

   if -1.01999999999999997e-144 < t < -4.99999999999999983e-275

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 41.2

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.2%

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]

   if -4.99999999999999983e-275 < t < 2.1000000000000001e-169

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]

      2. lower-*.f64 42.6

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]

   9. Applied rewrites 42.6%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]

   if 2.1000000000000001e-169 < t < 1.6e114

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   8. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      3. lower-*.f64 43.8

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   9. Applied rewrites 43.8%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 58.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.7 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z))))))
        (t_2 (* x (fma -4.0 i (* 18.0 (* t (* y z)))))))
   (if (<= x -1.05e+86)
     t_2
     (if (<= x -4.4e-21)
       t_1
       (if (<= x 7.7e-13)
         (fma c b (- (* (* j k) 27.0)))
         (if (<= x 2.35e+162) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double t_2 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -1.05e+86) {
		tmp = t_2;
	} else if (x <= -4.4e-21) {
		tmp = t_1;
	} else if (x <= 7.7e-13) {
		tmp = fma(c, b, -((j * k) * 27.0));
	} else if (x <= 2.35e+162) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	t_2 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -1.05e+86)
		tmp = t_2;
	elseif (x <= -4.4e-21)
		tmp = t_1;
	elseif (x <= 7.7e-13)
		tmp = fma(c, b, Float64(-Float64(Float64(j * k) * 27.0)));
	elseif (x <= 2.35e+162)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+86], t$95$2, If[LessEqual[x, -4.4e-21], t$95$1, If[LessEqual[x, 7.7e-13], N[(c * b + (-N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 2.35e+162], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0499999999999999e86 or 2.35000000000000001e162 < x

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, \color{blue}{i}, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.6

         \[\leadsto x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.6%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.0499999999999999e86 < x < -4.4000000000000001e-21 or 7.6999999999999995e-13 < x < 2.35000000000000001e162

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. lower-fma.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, \color{blue}{a}, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.4

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.4%

      \[\leadsto \color{blue}{t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -4.4000000000000001e-21 < x < 7.6999999999999995e-13

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      2. lower-*.f64 43.8

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 43.8%

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      2. sub-flip N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, \mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) \]

      6. lower-neg.f64 44.2

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right) \]

      9. lower-*.f64 44.2

         \[\leadsto \mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right) \]

   9. Applied rewrites 44.2%

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

Alternative 12: 54.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+86}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 k) j (* -4.0 (* a t)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -500000000000.0)
     t_1
     (if (<= t_2 1e+86) (- (* b c) (* 4.0 (* i x))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * k), j, (-4.0 * (a * t)));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -500000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 1e+86) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * k), j, Float64(-4.0 * Float64(a * t)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -500000000000.0)
		tmp = t_1;
	elseif (t_2 <= 1e+86)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * k), $MachinePrecision] * j + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -500000000000.0], t$95$1, If[LessEqual[t$95$2, 1e+86], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5e11 or 1e86 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, c \cdot b\right)\right)\right)} \]

   5. Applied rewrites 88.2%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\mathsf{fma}\left(\left(t \cdot \left(18 \cdot x\right)\right) \cdot z, y, \mathsf{fma}\left(t \cdot -4, a, \mathsf{fma}\left(-4 \cdot x, i, b \cdot c\right)\right)\right)}\right) \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{-4 \cdot \left(a \cdot t\right) + b \cdot c}\right) \]
   7. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, \color{blue}{a \cdot t}, b \cdot c\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot \color{blue}{t}, b \cdot c\right)\right) \]

      3. lower-*.f64 62.0

         \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right) \]

   8. Applied rewrites 62.0%

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, \color{blue}{\mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)}\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot \color{blue}{t}\right)\right) \]

       2. lower-*.f64 42.7

          \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \left(a \cdot t\right)\right) \]

   11. Applied rewrites 42.7%

       \[\leadsto \mathsf{fma}\left(-27 \cdot k, j, -4 \cdot \color{blue}{\left(a \cdot t\right)}\right) \]

   if -5e11 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e86

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 41.2

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.2%

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

Alternative 13: 54.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+200}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+200)
   (fma -27.0 (* j k) (* b c))
   (if (<= (* b c) 2e+124)
     (fma (* i -4.0) x (* -27.0 (* j k)))
     (- (* b c) (* 4.0 (* i x))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+200) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else if ((b * c) <= 2e+124) {
		tmp = fma((i * -4.0), x, (-27.0 * (j * k)));
	} else {
		tmp = (b * c) - (4.0 * (i * x));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4e+200)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	elseif (Float64(b * c) <= 2e+124)
		tmp = fma(Float64(i * -4.0), x, Float64(-27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4e+200], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+124], N[(N[(i * -4.0), $MachinePrecision] * x + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -3.9999999999999999e200

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   8. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      3. lower-*.f64 43.8

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   9. Applied rewrites 43.8%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if -3.9999999999999999e200 < (*.f64 b c) < 1.9999999999999999e124

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]

      2. lower-*.f64 42.6

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]

   9. Applied rewrites 42.6%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, x, -27 \cdot \left(j \cdot k\right)\right) \]

   if 1.9999999999999999e124 < (*.f64 b c)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 41.2

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.2%

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

Alternative 14: 54.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+33)
     (fma -27.0 (* j k) (* b c))
     (if (<= t_1 2e+18)
       (- (* b c) (* 4.0 (* i x)))
       (fma c b (- (* (* j k) 27.0)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+33) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else if (t_1 <= 2e+18) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = fma(c, b, -((j * k) * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+33)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	elseif (t_1 <= 2e+18)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = fma(c, b, Float64(-Float64(Float64(j * k) * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+33], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+18], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * b + (-N[(N[(j * k), $MachinePrecision] * 27.0), $MachinePrecision])), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   8. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      3. lower-*.f64 43.8

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   9. Applied rewrites 43.8%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if -1.9999999999999999e33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e18

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 41.2

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.2%

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]

   if 2e18 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      2. lower-*.f64 43.8

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 43.8%

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      2. sub-flip N/A

         \[\leadsto b \cdot c + \color{blue}{\left(\mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(\color{blue}{27 \cdot \left(j \cdot k\right)}\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, \mathsf{neg}\left(27 \cdot \left(j \cdot k\right)\right)\right) \]

      6. lower-neg.f64 44.2

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right) \]

      9. lower-*.f64 44.2

         \[\leadsto \mathsf{fma}\left(c, b, -\left(j \cdot k\right) \cdot 27\right) \]

   9. Applied rewrites 44.2%

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

Alternative 15: 54.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+33)
     (fma -27.0 (* j k) (* b c))
     (if (<= t_1 2e+18)
       (- (* b c) (* 4.0 (* i x)))
       (- (* b c) (* (* 27.0 j) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+33) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else if (t_1 <= 2e+18) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = (b * c) - ((27.0 * j) * k);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+33)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	elseif (t_1 <= 2e+18)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * j) * k));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+33], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+18], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * j), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   8. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      3. lower-*.f64 43.8

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   9. Applied rewrites 43.8%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if -1.9999999999999999e33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e18

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 41.2

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.2%

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]

   if 2e18 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      2. lower-*.f64 43.8

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

   7. Applied rewrites 43.8%

      \[\leadsto b \cdot c - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot c - 27 \cdot \left(j \cdot k\right) \]

      3. associate-*r* N/A

         \[\leadsto b \cdot c - \left(27 \cdot j\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto b \cdot c - \left(j \cdot 27\right) \cdot k \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(j \cdot 27\right) \cdot k \]

      6. *-commutative N/A

         \[\leadsto b \cdot c - \left(27 \cdot j\right) \cdot k \]

      7. lower-*.f64 43.8

         \[\leadsto b \cdot c - \left(27 \cdot j\right) \cdot k \]

   9. Applied rewrites 43.8%

      \[\leadsto b \cdot c - \left(27 \cdot j\right) \cdot k \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 54.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* j k) (* b c))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+33)
     t_1
     (if (<= t_2 2e+18) (- (* b c) (* 4.0 (* i x))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (j * k), (b * c));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+33) {
		tmp = t_1;
	} else if (t_2 <= 2e+18) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(j * k), Float64(b * c))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+33)
		tmp = t_1;
	elseif (t_2 <= 2e+18)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+33], t$95$1, If[LessEqual[t$95$2, 2e+18], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999999e33 or 2e18 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   8. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      3. lower-*.f64 43.8

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   9. Applied rewrites 43.8%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if -1.9999999999999999e33 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e18

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot c - 4 \cdot \color{blue}{\left(i \cdot x\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot \color{blue}{x}\right) \]

      2. lower-*.f64 41.2

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.2%

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

Alternative 17: 47.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(i \cdot x\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+195}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* i x))))
   (if (<= x -2.1e+172)
     t_1
     (if (<= x 9.5e+195) (fma -27.0 (* j k) (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (i * x);
	double tmp;
	if (x <= -2.1e+172) {
		tmp = t_1;
	} else if (x <= 9.5e+195) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(i * x))
	tmp = 0.0
	if (x <= -2.1e+172)
		tmp = t_1;
	elseif (x <= 9.5e+195)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+172], t$95$1, If[LessEqual[x, 9.5e+195], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e172 or 9.5000000000000004e195 < x

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. lower-*.f64 21.5

         \[\leadsto -4 \cdot \left(i \cdot \color{blue}{x}\right) \]

   4. Applied rewrites 21.5%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if -2.1000000000000001e172 < x < 9.5000000000000004e195

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, \color{blue}{i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot \color{blue}{x}, 27 \cdot \left(j \cdot k\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 61.1

         \[\leadsto b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right) \]

   4. Applied rewrites 61.1%

      \[\leadsto \color{blue}{b \cdot c - \mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\mathsf{fma}\left(4, i \cdot x, 27 \cdot \left(j \cdot k\right)\right)} \]

      2. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      3. associate--r+ N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \color{blue}{\left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)} \]

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

         \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) + \color{blue}{\left(\mathsf{neg}\left(27\right)\right)} \cdot \left(j \cdot k\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      9. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      10. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right) \]

      12. metadata-eval N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(\color{blue}{j} \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      14. *-commutative N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      15. associate-*l* N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

      16. lift-*.f64 N/A

          \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) + \left(-27 \cdot k\right) \cdot j \]

      17. +-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) + \color{blue}{\left(-27 \cdot k\right)} \cdot j \]

      18. associate-+l+ N/A

          \[\leadsto \left(-4 \cdot x\right) \cdot i + \color{blue}{\left(b \cdot c + \left(-27 \cdot k\right) \cdot j\right)} \]

   6. Applied rewrites 62.1%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, \mathsf{fma}\left(b, c, \left(j \cdot k\right) \cdot -27\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto -27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c} \]
   8. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      3. lower-*.f64 43.8

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   9. Applied rewrites 43.8%

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

Alternative 18: 35.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+111}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t\_1 \leq 2000:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+111)
     (* -27.0 (* j k))
     (if (<= t_1 2000.0) (* -4.0 (* i x)) (* (* j -27.0) k)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+111) {
		tmp = -27.0 * (j * k);
	} else if (t_1 <= 2000.0) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = (j * -27.0) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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, c, i, j, k)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+111)) then
        tmp = (-27.0d0) * (j * k)
    else if (t_1 <= 2000.0d0) then
        tmp = (-4.0d0) * (i * x)
    else
        tmp = (j * (-27.0d0)) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+111) {
		tmp = -27.0 * (j * k);
	} else if (t_1 <= 2000.0) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = (j * -27.0) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+111:
		tmp = -27.0 * (j * k)
	elif t_1 <= 2000.0:
		tmp = -4.0 * (i * x)
	else:
		tmp = (j * -27.0) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+111)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (t_1 <= 2000.0)
		tmp = Float64(-4.0 * Float64(i * x));
	else
		tmp = Float64(Float64(j * -27.0) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+111)
		tmp = -27.0 * (j * k);
	elseif (t_1 <= 2000.0)
		tmp = -4.0 * (i * x);
	else
		tmp = (j * -27.0) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+111], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2000.0], N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision], N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999991e111

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. lower-*.f64 24.0

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

   4. Applied rewrites 24.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -1.99999999999999991e111 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e3

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. lower-*.f64 21.5

         \[\leadsto -4 \cdot \left(i \cdot \color{blue}{x}\right) \]

   4. Applied rewrites 21.5%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 2e3 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. lower-*.f64 24.0

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

   4. Applied rewrites 24.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(j \cdot k\right) \cdot \color{blue}{-27} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(j \cdot k\right) \cdot -27 \]

      4. *-commutative N/A

         \[\leadsto \left(k \cdot j\right) \cdot -27 \]

      5. associate-*l* N/A

         \[\leadsto k \cdot \color{blue}{\left(j \cdot -27\right)} \]

      6. *-commutative N/A

         \[\leadsto \left(j \cdot -27\right) \cdot \color{blue}{k} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(j \cdot -27\right) \cdot \color{blue}{k} \]

      8. lower-*.f64 24.0

         \[\leadsto \left(j \cdot -27\right) \cdot k \]

   6. Applied rewrites 24.0%

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

Alternative 19: 35.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2000:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+111) t_1 (if (<= t_2 2000.0) (* -4.0 (* i x)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+111) {
		tmp = t_1;
	} else if (t_2 <= 2000.0) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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, c, i, j, k)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+111)) then
        tmp = t_1
    else if (t_2 <= 2000.0d0) then
        tmp = (-4.0d0) * (i * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+111) {
		tmp = t_1;
	} else if (t_2 <= 2000.0) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+111:
		tmp = t_1
	elif t_2 <= 2000.0:
		tmp = -4.0 * (i * x)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+111)
		tmp = t_1;
	elseif (t_2 <= 2000.0)
		tmp = Float64(-4.0 * Float64(i * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+111)
		tmp = t_1;
	elseif (t_2 <= 2000.0)
		tmp = -4.0 * (i * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+111], t$95$1, If[LessEqual[t$95$2, 2000.0], N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999991e111 or 2e3 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. lower-*.f64 24.0

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

   4. Applied rewrites 24.0%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -1.99999999999999991e111 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e3

   1. Initial program 85.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. lower-*.f64 21.5

         \[\leadsto -4 \cdot \left(i \cdot \color{blue}{x}\right) \]

   4. Applied rewrites 21.5%

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

Alternative 20: 24.0% accurate, 6.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ -27 \cdot \left(j \cdot k\right) \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return -27.0 * (j * k);
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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, c, i, j, k)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (-27.0d0) * (j * k)
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return -27.0 * (j * k);
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return -27.0 * (j * k)

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(-27.0 * Float64(j * k))
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = -27.0 * (j * k);
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.3%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

2. Taylor expanded in j around inf

   \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

   2. lower-*.f64 24.0

      \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

4. Applied rewrites 24.0%

   \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025155 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))