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

Percentage Accurate: 84.9% → 92.4%

Time: 6.5s

Alternatives: 12

Speedup: 0.6×

• 50.4% 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: 84.9% 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: 92.4% accurate, 0.6× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
       (* (* x 4.0) i))
      INFINITY)
   (fma
    (* -27.0 j)
    k
    (fma (* 18.0 t) (* (* y x) z) (- (* c b) (* 4.0 (fma a t (* i x))))))
   (- (* (fma -18.0 (* (* t y) z) (* i 4.0)) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) <= ((double) INFINITY)) {
		tmp = fma((-27.0 * j), k, fma((18.0 * t), ((y * x) * z), ((c * b) - (4.0 * fma(a, t, (i * x))))));
	} else {
		tmp = -(fma(-18.0, ((t * y) * z), (i * 4.0)) * 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])
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(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)) <= Inf)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(18.0 * t), Float64(Float64(y * x) * z), Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x))))));
	else
		tmp = Float64(-Float64(fma(-18.0, Float64(Float64(t * y) * z), Float64(i * 4.0)) * 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.
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[(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], Infinity], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(18.0 * t), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + N[(i * 4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < +inf.0

   1. Initial program 92.5%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 92.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 94.0

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

   6. Applied rewrites 94.0%

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

   if +inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 0.0%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 74.1

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

   4. Applied rewrites 74.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 74.8

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

   6. Applied rewrites 74.8%

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

Alternative 2: 78.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -\mathsf{fma}\left(-18, \left(t \cdot y\right) \cdot z, i \cdot 4\right) \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -18.0 (* (* t y) z) (* i 4.0)) x))))
   (if (<= x -2.6e+124)
     t_1
     (if (<= x 5.8e+107)
       (- (* c b) (fma 4.0 (fma a t (* i x)) (* (* k j) 27.0)))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(-18.0, ((t * y) * z), (i * 4.0)) * x);
	double tmp;
	if (x <= -2.6e+124) {
		tmp = t_1;
	} else if (x <= 5.8e+107) {
		tmp = (c * b) - fma(4.0, fma(a, t, (i * x)), ((k * j) * 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])
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(fma(-18.0, Float64(Float64(t * y) * z), Float64(i * 4.0)) * x))
	tmp = 0.0
	if (x <= -2.6e+124)
		tmp = t_1;
	elseif (x <= 5.8e+107)
		tmp = Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), Float64(Float64(k * j) * 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.
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[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + N[(i * 4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[x, -2.6e+124], t$95$1, If[LessEqual[x, 5.8e+107], N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e124 or 5.79999999999999975e107 < x

   1. Initial program 69.9%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 73.4

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

   4. Applied rewrites 73.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 73.5

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

   6. Applied rewrites 73.5%

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

   if -2.6e124 < x < 5.79999999999999975e107

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 81.0

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

   4. Applied rewrites 81.0%

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

Alternative 3: 72.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4 \cdot i, x, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 x) z) 18.0 (* -4.0 a)) t)))
   (if (<= t -1.6e+24)
     t_1
     (if (<= t 7.8e+72) (fma (* -27.0 j) k (fma (* -4.0 i) x (* c b))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * x) * z), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -1.6e+24) {
		tmp = t_1;
	} else if (t <= 7.8e+72) {
		tmp = fma((-27.0 * j), k, fma((-4.0 * i), x, (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])
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(fma(Float64(Float64(y * x) * z), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -1.6e+24)
		tmp = t_1;
	elseif (t <= 7.8e+72)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(-4.0 * i), x, 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.
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[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.6e+24], t$95$1, If[LessEqual[t, 7.8e+72], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5999999999999999e24 or 7.79999999999999984e72 < t

   1. Initial program 82.8%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 86.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 86.8

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

   6. Applied rewrites 86.8%

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

   7. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right) \cdot t \]

      4. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18 + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right) \cdot t \]

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. lower-*.f64 67.7

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

   9. Applied rewrites 67.7%

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

   if -1.5999999999999999e24 < t < 7.79999999999999984e72

   1. Initial program 86.4%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 86.8%

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

   5. Taylor expanded in t around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 75.3

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

   7. Applied rewrites 75.3%

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

Alternative 4: 68.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -\mathsf{fma}\left(-18, \left(t \cdot y\right) \cdot z, i \cdot 4\right) \cdot x\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -18.0 (* (* t y) z) (* i 4.0)) x))))
   (if (<= x -1.9e+123)
     t_1
     (if (<= x 5.8e+107) (fma c b (* -4.0 (fma i x (* a t)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(-18.0, ((t * y) * z), (i * 4.0)) * x);
	double tmp;
	if (x <= -1.9e+123) {
		tmp = t_1;
	} else if (x <= 5.8e+107) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t))));
	} 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])
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(fma(-18.0, Float64(Float64(t * y) * z), Float64(i * 4.0)) * x))
	tmp = 0.0
	if (x <= -1.9e+123)
		tmp = t_1;
	elseif (x <= 5.8e+107)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))));
	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.
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[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] + N[(i * 4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[x, -1.9e+123], t$95$1, If[LessEqual[x, 5.8e+107], N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.89999999999999997e123 or 5.79999999999999975e107 < x

   1. Initial program 70.0%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 73.4

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

   4. Applied rewrites 73.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 73.4

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

   6. Applied rewrites 73.4%

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

   if -1.89999999999999997e123 < x < 5.79999999999999975e107

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 81.0

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

   4. Applied rewrites 81.0%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.4

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

   7. Applied rewrites 59.4%

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

Alternative 5: 63.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* c b))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+204)
     t_1
     (if (<= t_2 1e+75) (fma c b (* -4.0 (fma i x (* a t)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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, (c * b));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+204) {
		tmp = t_1;
	} else if (t_2 <= 1e+75) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t))));
	} 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])
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 * j), k, Float64(c * b))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+204)
		tmp = t_1;
	elseif (t_2 <= 1e+75)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))));
	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.
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 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+204], t$95$1, If[LessEqual[t$95$2, 1e+75], N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.99999999999999998e204 or 9.99999999999999927e74 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.9%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 66.9

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

   7. Applied rewrites 66.9%

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

   if -1.99999999999999998e204 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999927e74

   1. Initial program 87.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.6

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

   4. Applied rewrites 74.6%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 68.5

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

   7. Applied rewrites 68.5%

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

Alternative 6: 54.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, -4 \cdot \left(i \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -2e-5)
   (fma (* k j) -27.0 (* c b))
   (if (<= (* b c) 2e+94)
     (fma (* -27.0 j) k (* -4.0 (* i x)))
     (fma (* -27.0 j) k (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) <= -2e-5) {
		tmp = fma((k * j), -27.0, (c * b));
	} else if ((b * c) <= 2e+94) {
		tmp = fma((-27.0 * j), k, (-4.0 * (i * x)));
	} else {
		tmp = fma((-27.0 * j), k, (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])
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) <= -2e-5)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	elseif (Float64(b * c) <= 2e+94)
		tmp = fma(Float64(-27.0 * j), k, Float64(-4.0 * Float64(i * x)));
	else
		tmp = fma(Float64(-27.0 * j), k, 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.
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], -2e-5], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+94], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.00000000000000016e-5

   1. Initial program 83.3%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 85.5%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 55.5

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

   7. Applied rewrites 55.5%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 55.0

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

   9. Applied rewrites 55.0%

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

   if -2.00000000000000016e-5 < (*.f64 b c) < 2e94

   1. Initial program 86.7%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lift-*.f64 50.7

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

   7. Applied rewrites 50.7%

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

   if 2e94 < (*.f64 b c)

   1. Initial program 81.3%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 83.9%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 64.1

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

   7. Applied rewrites 64.1%

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

Alternative 7: 48.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+123}:\\ \;\;\;\;-\left(\left(\left(t \cdot y\right) \cdot -18\right) \cdot z\right) \cdot x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -7.5e+123)
   (- (* (* (* (* t y) -18.0) z) x))
   (if (<= x 1.9e+108)
     (fma (* -27.0 j) k (* c b))
     (* (* (* (* y x) z) t) 18.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -7.5e+123) {
		tmp = -((((t * y) * -18.0) * z) * x);
	} else if (x <= 1.9e+108) {
		tmp = fma((-27.0 * j), k, (c * b));
	} else {
		tmp = (((y * x) * z) * t) * 18.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -7.5e+123)
		tmp = Float64(-Float64(Float64(Float64(Float64(t * y) * -18.0) * z) * x));
	elseif (x <= 1.9e+108)
		tmp = fma(Float64(-27.0 * j), k, Float64(c * b));
	else
		tmp = Float64(Float64(Float64(Float64(y * x) * z) * t) * 18.0);
	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.
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, -7.5e+123], (-N[(N[(N[(N[(t * y), $MachinePrecision] * -18.0), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision]), If[LessEqual[x, 1.9e+108], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4999999999999999e123

   1. Initial program 70.6%

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

   2. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

         \[\leadsto -x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right) \cdot x \]

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 73.6

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

   4. Applied rewrites 73.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 72.9

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

   7. Applied rewrites 72.9%

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

   8. Taylor expanded in y around inf

      \[\leadsto -\left(\left(-18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -\left(\left(\left(t \cdot y\right) \cdot -18\right) \cdot z\right) \cdot x \]

      2. lift-*.f64 N/A

         \[\leadsto -\left(\left(\left(t \cdot y\right) \cdot -18\right) \cdot z\right) \cdot x \]

      3. lift-*.f64 44.3

         \[\leadsto -\left(\left(\left(t \cdot y\right) \cdot -18\right) \cdot z\right) \cdot x \]

   10. Applied rewrites 44.3%

       \[\leadsto -\left(\left(\left(t \cdot y\right) \cdot -18\right) \cdot z\right) \cdot x \]

   if -7.4999999999999999e123 < x < 1.90000000000000004e108

   1. Initial program 91.6%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 90.1%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 50.6

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

   7. Applied rewrites 50.6%

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

   if 1.90000000000000004e108 < x

   1. Initial program 69.2%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 78.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.0

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

   6. Applied rewrites 74.0%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      8. lift-*.f64 42.8

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

   9. Applied rewrites 42.8%

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

Alternative 8: 48.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* (* (* (* y x) z) t) 18.0)))
   (if (<= x -7.5e+123)
     t_1
     (if (<= x 1.9e+108) (fma (* -27.0 j) k (* c b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = (((y * x) * z) * t) * 18.0;
	double tmp;
	if (x <= -7.5e+123) {
		tmp = t_1;
	} else if (x <= 1.9e+108) {
		tmp = fma((-27.0 * j), k, (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])
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(y * x) * z) * t) * 18.0)
	tmp = 0.0
	if (x <= -7.5e+123)
		tmp = t_1;
	elseif (x <= 1.9e+108)
		tmp = fma(Float64(-27.0 * j), k, 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.
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[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]}, If[LessEqual[x, -7.5e+123], t$95$1, If[LessEqual[x, 1.9e+108], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4999999999999999e123 or 1.90000000000000004e108 < x

   1. Initial program 69.9%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 79.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 74.0

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

   6. Applied rewrites 74.0%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right) \cdot 18 \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      8. lift-*.f64 43.5

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

   9. Applied rewrites 43.5%

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

   if -7.4999999999999999e123 < x < 1.90000000000000004e108

   1. Initial program 91.6%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 90.1%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 50.6

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

   7. Applied rewrites 50.6%

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

Alternative 9: 46.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \left(i \cdot 4\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
       (* (* x 4.0) i))
      1e+296)
   (fma (* k j) -27.0 (* c b))
   (- (* c b) (* (* i 4.0) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) <= 1e+296) {
		tmp = fma((k * j), -27.0, (c * b));
	} else {
		tmp = (c * b) - ((i * 4.0) * 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])
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(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)) <= 1e+296)
		tmp = fma(Float64(k * j), -27.0, Float64(c * b));
	else
		tmp = Float64(Float64(c * b) - Float64(Float64(i * 4.0) * 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.
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[(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], 1e+296], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(N[(i * 4.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 9.99999999999999981e295

   1. Initial program 95.3%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 48.8

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

   7. Applied rewrites 48.8%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 48.6

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

   9. Applied rewrites 48.6%

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

   if 9.99999999999999981e295 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 60.2%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 57.1

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

   4. Applied rewrites 57.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 42.4

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

   7. Applied rewrites 42.4%

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

Alternative 10: 45.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -5.3 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* a t))))
   (if (<= t -5.3e+35)
     t_1
     (if (<= t 1.36e+75) (fma (* -27.0 j) k (* c b)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * (a * t);
	double tmp;
	if (t <= -5.3e+35) {
		tmp = t_1;
	} else if (t <= 1.36e+75) {
		tmp = fma((-27.0 * j), k, (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])
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(a * t))
	tmp = 0.0
	if (t <= -5.3e+35)
		tmp = t_1;
	elseif (t <= 1.36e+75)
		tmp = fma(Float64(-27.0 * j), k, 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.
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[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.3e+35], t$95$1, If[LessEqual[t, 1.36e+75], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.30000000000000009e35 or 1.36e75 < t

   1. Initial program 82.6%

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

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 34.7

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 34.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if -5.30000000000000009e35 < t < 1.36e75

   1. Initial program 86.5%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 86.9%

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

   5. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 52.9

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

   7. Applied rewrites 52.9%

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

Alternative 11: 36.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+43}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+127}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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) -1e+43)
   (* c b)
   (if (<= (* b c) 5e+127) (* -27.0 (* k j)) (* c b))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) <= -1e+43) {
		tmp = c * b;
	} else if ((b * c) <= 5e+127) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	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.
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) :: tmp
    if ((b * c) <= (-1d+43)) then
        tmp = c * b
    else if ((b * c) <= 5d+127) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    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;
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 tmp;
	if ((b * c) <= -1e+43) {
		tmp = c * b;
	} else if ((b * c) <= 5e+127) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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):
	tmp = 0
	if (b * c) <= -1e+43:
		tmp = c * b
	elif (b * c) <= 5e+127:
		tmp = -27.0 * (k * j)
	else:
		tmp = 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])
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) <= -1e+43)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 5e+127)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	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])){:}
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)
	tmp = 0.0;
	if ((b * c) <= -1e+43)
		tmp = c * b;
	elseif ((b * c) <= 5e+127)
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	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.
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], -1e+43], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+127], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.00000000000000001e43 or 5.0000000000000004e127 < (*.f64 b c)

   1. Initial program 81.9%

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

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 51.3

         \[\leadsto c \cdot \color{blue}{b} \]

   4. Applied rewrites 51.3%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -1.00000000000000001e43 < (*.f64 b c) < 5.0000000000000004e127

   1. Initial program 86.6%

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

   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. *-commutative N/A

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

      3. lower-*.f64 27.5

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

   4. Applied rewrites 27.5%

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

Alternative 12: 23.4% accurate, 11.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* c b))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 c * b;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 = c * b
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 c * b;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[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 c * b

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(c * b)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
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 = c * b;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(c * b), $MachinePrecision]

Derivation

1. Initial program 84.9%

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

2. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto c \cdot \color{blue}{b} \]

   2. lower-*.f64 23.4

      \[\leadsto c \cdot \color{blue}{b} \]

4. Applied rewrites 23.4%

   \[\leadsto \color{blue}{c \cdot b} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025114 
(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)))