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

Percentage Accurate: 85.9% → 93.8%

Time: 8.8s

Alternatives: 23

Speedup: 0.5×

• 50.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% 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: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(k \cdot j\right) \cdot 27\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - t\_2\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot z, x \cdot 18, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\right)\right) - t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot y\right) \cdot 18, z, a \cdot -4\right), t, c \cdot b - \left(4 \cdot x\right) \cdot i\right) - t\_1\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-18 \cdot t, y \cdot x, \frac{c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), t\_1\right)}{-z}\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* k j) 27.0))
        (t_2 (* (* j 27.0) k))
        (t_3
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
           (* (* x 4.0) i))
          t_2)))
   (if (<= t_3 (- INFINITY))
     (-
      (fma
       (* (* y t) z)
       (* x 18.0)
       (fma (* -4.0 a) t (fma (* i x) -4.0 (* c b))))
      t_2)
     (if (<= t_3 2e+300)
       (-
        (fma (fma (* (* x y) 18.0) z (* a -4.0)) t (- (* c b) (* (* 4.0 x) i)))
        t_1)
       (if (<= t_3 INFINITY)
         (*
          (fma
           (* -18.0 t)
           (* y x)
           (/ (- (* c b) (fma 4.0 (fma a t (* i x)) t_1)) (- z)))
          (- z))
         (* (fma (* 18.0 t) (* z y) (* -4.0 i)) 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 t_1 = (k * j) * 27.0;
	double t_2 = (j * 27.0) * k;
	double t_3 = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = fma(((y * t) * z), (x * 18.0), fma((-4.0 * a), t, fma((i * x), -4.0, (c * b)))) - t_2;
	} else if (t_3 <= 2e+300) {
		tmp = fma(fma(((x * y) * 18.0), z, (a * -4.0)), t, ((c * b) - ((4.0 * x) * i))) - t_1;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = fma((-18.0 * t), (y * x), (((c * b) - fma(4.0, fma(a, t, (i * x)), t_1)) / -z)) * -z;
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(k * j) * 27.0)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = 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)) - t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(fma(Float64(Float64(y * t) * z), Float64(x * 18.0), fma(Float64(-4.0 * a), t, fma(Float64(i * x), -4.0, Float64(c * b)))) - t_2);
	elseif (t_3 <= 2e+300)
		tmp = Float64(fma(fma(Float64(Float64(x * y) * 18.0), z, Float64(a * -4.0)), t, Float64(Float64(c * b) - Float64(Float64(4.0 * x) * i))) - t_1);
	elseif (t_3 <= Inf)
		tmp = Float64(fma(Float64(-18.0 * t), Float64(y * x), Float64(Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), t_1)) / Float64(-z))) * Float64(-z));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = 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] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(N[(y * t), $MachinePrecision] * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 2e+300], N[(N[(N[(N[(N[(x * y), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(N[(N[(-18.0 * t), $MachinePrecision] * N[(y * x), $MachinePrecision] + N[(N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision] * (-z)), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < -inf.0

   1. Initial program 86.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 90.8

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

   4. Applied rewrites 90.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. lift-neg.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. metadata-eval N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 98.2%

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

   8. Applied rewrites 96.8%

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

   if -inf.0 < (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < 2.0000000000000001e300

   1. Initial program 98.9%

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

   4. Applied rewrites 95.3%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 99.0

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

   6. Applied rewrites 99.0%

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

   if 2.0000000000000001e300 < (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 89.8%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)}{z}\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(-18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)}{z}\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -z \cdot \left(-18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)}{z}\right) \cdot z \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(t \cdot \left(x \cdot y\right)\right) + -1 \cdot \frac{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)}{z}\right) \cdot z \]

   5. Applied rewrites 91.4%

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

   if +inf.0 < (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot t\right) \cdot z, x \cdot 18, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot y\right) \cdot 18, z, a \cdot -4\right), t, c \cdot b - \left(4 \cdot x\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-18 \cdot t, y \cdot x, \frac{c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)}{-z}\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.2% accurate, 0.3× speedup

Math

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

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
 (let* ((t_1 (* (* j 27.0) k))
        (t_2
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
           (* (* x 4.0) i))
          t_1)))
   (if (<= t_2 (- INFINITY))
     (-
      (fma
       (* (* y t) z)
       (* x 18.0)
       (fma (* -4.0 a) t (fma (* i x) -4.0 (* c b))))
      t_1)
     (if (<= t_2 INFINITY)
       (-
        (fma (fma (* (* x y) 18.0) z (* a -4.0)) t (- (* c b) (* (* 4.0 x) i)))
        (* (* k j) 27.0))
       (* (fma (* 18.0 t) (* z y) (* -4.0 i)) 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 t_1 = (j * 27.0) * k;
	double t_2 = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(((y * t) * z), (x * 18.0), fma((-4.0 * a), t, fma((i * x), -4.0, (c * b)))) - t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma(fma(((x * y) * 18.0), z, (a * -4.0)), t, ((c * b) - ((4.0 * x) * i))) - ((k * j) * 27.0);
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = 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)) - t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(fma(Float64(Float64(y * t) * z), Float64(x * 18.0), fma(Float64(-4.0 * a), t, fma(Float64(i * x), -4.0, Float64(c * b)))) - t_1);
	elseif (t_2 <= Inf)
		tmp = Float64(fma(fma(Float64(Float64(x * y) * 18.0), z, Float64(a * -4.0)), t, Float64(Float64(c * b) - Float64(Float64(4.0 * x) * i))) - Float64(Float64(k * j) * 27.0));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < -inf.0

   1. Initial program 86.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 90.8

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

   4. Applied rewrites 90.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. lift-neg.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. metadata-eval N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 98.2%

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

   8. Applied rewrites 96.8%

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

   if -inf.0 < (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 95.8%

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

   4. Applied rewrites 92.9%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 95.9

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

   6. Applied rewrites 95.9%

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

   if +inf.0 < (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

Alternative 3: 92.2% accurate, 0.5× speedup

Math

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

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))
       (* (* j 27.0) k))
      INFINITY)
   (-
    (fma (fma (* (* x y) 18.0) z (* a -4.0)) t (- (* c b) (* (* 4.0 x) i)))
    (* (* k j) 27.0))
   (* (fma (* 18.0 t) (* z y) (* -4.0 i)) 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)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = fma(fma(((x * y) * 18.0), z, (a * -4.0)), t, ((c * b) - ((4.0 * x) * i))) - ((k * j) * 27.0);
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(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)) <= Inf)
		tmp = Float64(fma(fma(Float64(Float64(x * y) * 18.0), z, Float64(a * -4.0)), t, Float64(Float64(c * b) - Float64(Float64(4.0 * x) * i))) - Float64(Float64(k * j) * 27.0));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(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], Infinity], N[(N[(N[(N[(N[(x * y), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 93.2%

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

   4. Applied rewrites 92.3%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 93.2

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

   6. Applied rewrites 93.2%

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

   if +inf.0 < (-.f64 (-.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)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

Alternative 4: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, \mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, b \cdot c\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 0.001:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot a\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* (* z y) x)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -1e+37)
     (fma (* 18.0 t) t_1 (fma (* -27.0 j) k (fma (* i x) -4.0 (* b c))))
     (if (<= t_2 0.001)
       (fma (* 18.0 t) t_1 (- (* c b) (* 4.0 (fma a t (* i x)))))
       (fma (* -27.0 j) k (fma (fma t_1 18.0 (* -4.0 a)) t (* 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 t_1 = (z * y) * x;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+37) {
		tmp = fma((18.0 * t), t_1, fma((-27.0 * j), k, fma((i * x), -4.0, (b * c))));
	} else if (t_2 <= 0.001) {
		tmp = fma((18.0 * t), t_1, ((c * b) - (4.0 * fma(a, t, (i * x)))));
	} else {
		tmp = fma((-27.0 * j), k, fma(fma(t_1, 18.0, (-4.0 * a)), t, (c * b)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(z * y) * x)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -1e+37)
		tmp = fma(Float64(18.0 * t), t_1, fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, Float64(b * c))));
	elseif (t_2 <= 0.001)
		tmp = fma(Float64(18.0 * t), t_1, Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(fma(t_1, 18.0, Float64(-4.0 * a)), t, Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+37], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.001], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999954e36

   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. Add Preprocessing

   4. Applied rewrites 86.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 87.9

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

   6. Applied rewrites 87.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 89.4%

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

   if -9.99999999999999954e36 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1e-3

   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. Add Preprocessing

   3. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

   if 1e-3 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 73.1%

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

   4. Applied rewrites 75.1%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 78.7

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

   6. Applied rewrites 78.7%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 72.0%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-fma.f64 N/A

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

       5. lift-*.f64 N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. *-commutative N/A

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

       10. associate-*r* N/A

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

   11. Applied rewrites 77.4%

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

Alternative 5: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+202}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-81} \lor \neg \left(x \leq 2.5 \cdot 10^{+41}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 -6.6e+202)
   (-
    (fma (fma (* (* z y) x) 18.0 (* -4.0 a)) t (* (* i x) -4.0))
    (* (* k j) 27.0))
   (if (or (<= x -1.02e-81) (not (<= x 2.5e+41)))
     (-
      (- (fma (* 18.0 x) (* y (* t z)) (* c b)) (* (* x 4.0) i))
      (* (* j 27.0) k))
     (fma (* j k) -27.0 (fma (fma (* (* y x) 18.0) z (* -4.0 a)) t (* b c))))))

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 <= -6.6e+202) {
		tmp = fma(fma(((z * y) * x), 18.0, (-4.0 * a)), t, ((i * x) * -4.0)) - ((k * j) * 27.0);
	} else if ((x <= -1.02e-81) || !(x <= 2.5e+41)) {
		tmp = (fma((18.0 * x), (y * (t * z)), (c * b)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = fma((j * k), -27.0, fma(fma(((y * x) * 18.0), z, (-4.0 * a)), t, (b * c)));
	}
	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 <= -6.6e+202)
		tmp = Float64(fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)) - Float64(Float64(k * j) * 27.0));
	elseif ((x <= -1.02e-81) || !(x <= 2.5e+41))
		tmp = Float64(Float64(fma(Float64(18.0 * x), Float64(y * Float64(t * z)), Float64(c * b)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(j * k), -27.0, fma(fma(Float64(Float64(y * x) * 18.0), z, Float64(-4.0 * a)), t, Float64(b * c)));
	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, -6.6e+202], N[(N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.02e-81], N[Not[LessEqual[x, 2.5e+41]], $MachinePrecision]], N[(N[(N[(N[(18.0 * x), $MachinePrecision] * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5999999999999998e202

   1. Initial program 54.6%

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

   4. Applied rewrites 63.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 81.9

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

   7. Applied rewrites 81.9%

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

   if -6.5999999999999998e202 < x < -1.01999999999999998e-81 or 2.50000000000000011e41 < x

   1. Initial program 75.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 79.1

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

   4. Applied rewrites 79.1%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-*l* N/A

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

      9. lift-*.f64 N/A

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

      10. lift-neg.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. metadata-eval N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 88.3%

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

   7. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.8

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

   9. Applied rewrites 87.8%

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

   if -1.01999999999999998e-81 < x < 2.50000000000000011e41

   1. Initial program 91.7%

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

   4. Applied rewrites 89.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 93.4

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

   6. Applied rewrites 93.4%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 85.6%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lower-fma.f64 N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

       10. associate-*l* N/A

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

       11. *-commutative N/A

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

       12. associate-*r* N/A

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

       13. lower-fma.f64 N/A

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

       14. *-commutative N/A

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

       15. lower-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lower-*.f64 N/A

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

       18. lift-*.f64 89.6

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

   11. Applied rewrites 89.6%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+202}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-81} \lor \neg \left(x \leq 2.5 \cdot 10^{+41}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot i\right) \cdot x\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+181}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -1 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-305}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-162}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* -4.0 i) x)))
   (if (<= (* b c) -5e+181)
     (* c b)
     (if (<= (* b c) -1e-196)
       t_1
       (if (<= (* b c) 5e-305)
         (* -4.0 (* a t))
         (if (<= (* b c) 1e-162)
           (* (* -27.0 k) j)
           (if (<= (* b c) 2e+71) t_1 (* 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 t_1 = (-4.0 * i) * x;
	double tmp;
	if ((b * c) <= -5e+181) {
		tmp = c * b;
	} else if ((b * c) <= -1e-196) {
		tmp = t_1;
	} else if ((b * c) <= 5e-305) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 1e-162) {
		tmp = (-27.0 * k) * j;
	} else if ((b * c) <= 2e+71) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = ((-4.0d0) * i) * x
    if ((b * c) <= (-5d+181)) then
        tmp = c * b
    else if ((b * c) <= (-1d-196)) then
        tmp = t_1
    else if ((b * c) <= 5d-305) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 1d-162) then
        tmp = ((-27.0d0) * k) * j
    else if ((b * c) <= 2d+71) then
        tmp = t_1
    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 t_1 = (-4.0 * i) * x;
	double tmp;
	if ((b * c) <= -5e+181) {
		tmp = c * b;
	} else if ((b * c) <= -1e-196) {
		tmp = t_1;
	} else if ((b * c) <= 5e-305) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 1e-162) {
		tmp = (-27.0 * k) * j;
	} else if ((b * c) <= 2e+71) {
		tmp = t_1;
	} 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):
	t_1 = (-4.0 * i) * x
	tmp = 0
	if (b * c) <= -5e+181:
		tmp = c * b
	elif (b * c) <= -1e-196:
		tmp = t_1
	elif (b * c) <= 5e-305:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 1e-162:
		tmp = (-27.0 * k) * j
	elif (b * c) <= 2e+71:
		tmp = t_1
	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)
	t_1 = Float64(Float64(-4.0 * i) * x)
	tmp = 0.0
	if (Float64(b * c) <= -5e+181)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -1e-196)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-305)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 1e-162)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (Float64(b * c) <= 2e+71)
		tmp = t_1;
	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)
	t_1 = (-4.0 * i) * x;
	tmp = 0.0;
	if ((b * c) <= -5e+181)
		tmp = c * b;
	elseif ((b * c) <= -1e-196)
		tmp = t_1;
	elseif ((b * c) <= 5e-305)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 1e-162)
		tmp = (-27.0 * k) * j;
	elseif ((b * c) <= 2e+71)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+181], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1e-196], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-305], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-162], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+71], t$95$1, N[(c * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.0000000000000003e181 or 2.0000000000000001e71 < (*.f64 b c)

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

   if -5.0000000000000003e181 < (*.f64 b c) < -1e-196 or 9.99999999999999954e-163 < (*.f64 b c) < 2.0000000000000001e71

   1. Initial program 86.0%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 37.0

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

   5. Applied rewrites 37.0%

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

   if -1e-196 < (*.f64 b c) < 4.99999999999999985e-305

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.0

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

   5. Applied rewrites 41.0%

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

   if 4.99999999999999985e-305 < (*.f64 b c) < 9.99999999999999954e-163

   1. Initial program 76.8%

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

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. 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 48.5

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

   5. Applied rewrites 48.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 48.6

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

   7. Applied rewrites 48.6%

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

Alternative 7: 81.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ \mathbf{if}\;t \leq -7 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot a\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-104}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (* (* z y) x)))
   (if (<= t -7e-68)
     (fma (* -27.0 j) k (fma (fma t_1 18.0 (* -4.0 a)) t (* c b)))
     (if (<= t 2.4e-104)
       (fma (* i x) -4.0 (fma c b (* (* j k) -27.0)))
       (fma (* 18.0 t) t_1 (- (* c b) (* 4.0 (fma a t (* i 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 t_1 = (z * y) * x;
	double tmp;
	if (t <= -7e-68) {
		tmp = fma((-27.0 * j), k, fma(fma(t_1, 18.0, (-4.0 * a)), t, (c * b)));
	} else if (t <= 2.4e-104) {
		tmp = fma((i * x), -4.0, fma(c, b, ((j * k) * -27.0)));
	} else {
		tmp = fma((18.0 * t), t_1, ((c * b) - (4.0 * fma(a, t, (i * x)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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(z * y) * x)
	tmp = 0.0
	if (t <= -7e-68)
		tmp = fma(Float64(-27.0 * j), k, fma(fma(t_1, 18.0, Float64(-4.0 * a)), t, Float64(c * b)));
	elseif (t <= 2.4e-104)
		tmp = fma(Float64(i * x), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	else
		tmp = fma(Float64(18.0 * t), t_1, Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[(z * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -7e-68], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-104], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000026e-68

   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. Add Preprocessing

   4. Applied rewrites 88.9%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 90.1

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

   6. Applied rewrites 90.1%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 84.1%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-fma.f64 N/A

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

       5. lift-*.f64 N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. *-commutative N/A

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

       10. associate-*r* N/A

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

   11. Applied rewrites 87.8%

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

   if -7.00000000000000026e-68 < t < 2.4000000000000001e-104

   1. Initial program 81.1%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 80.0

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

   5. Applied rewrites 80.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate--r+ N/A

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

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

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate--l+ N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. lower-fma.f64 N/A

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

   7. Applied rewrites 80.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 81.0

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

   9. Applied rewrites 81.0%

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

   if 2.4000000000000001e-104 < t

   1. Initial program 81.0%

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

   3. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 79.3

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

   5. Applied rewrites 79.3%

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

Alternative 8: 81.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, \left(i \cdot x\right) \cdot -4\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

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 -2.1e-21)
   (-
    (fma (fma (* (* z y) x) 18.0 (* -4.0 a)) t (* (* i x) -4.0))
    (* (* k j) 27.0))
   (if (<= x 3.6e+110)
     (fma (* j k) -27.0 (fma (fma (* (* y x) 18.0) z (* -4.0 a)) t (* b c)))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) 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 <= -2.1e-21) {
		tmp = fma(fma(((z * y) * x), 18.0, (-4.0 * a)), t, ((i * x) * -4.0)) - ((k * j) * 27.0);
	} else if (x <= 3.6e+110) {
		tmp = fma((j * k), -27.0, fma(fma(((y * x) * 18.0), z, (-4.0 * a)), t, (b * c)));
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2.1e-21)
		tmp = Float64(fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)), t, Float64(Float64(i * x) * -4.0)) - Float64(Float64(k * j) * 27.0));
	elseif (x <= 3.6e+110)
		tmp = fma(Float64(j * k), -27.0, fma(fma(Float64(Float64(y * x) * 18.0), z, Float64(-4.0 * a)), t, Float64(b * c)));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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, -2.1e-21], N[(N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+110], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.10000000000000013e-21

   1. Initial program 72.2%

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 80.6

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

   7. Applied rewrites 80.6%

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

   if -2.10000000000000013e-21 < x < 3.5999999999999997e110

   1. Initial program 90.4%

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

   4. Applied rewrites 89.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 92.5

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

   6. Applied rewrites 92.5%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 84.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lower-fma.f64 N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

       10. associate-*l* N/A

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

       11. *-commutative N/A

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

       12. associate-*r* N/A

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

       13. lower-fma.f64 N/A

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

       14. *-commutative N/A

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

       15. lower-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lower-*.f64 N/A

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

       18. lift-*.f64 88.0

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

   11. Applied rewrites 88.0%

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

   if 3.5999999999999997e110 < x

   1. Initial program 65.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 81.3

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

   5. Applied rewrites 81.3%

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

Alternative 9: 83.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-68} \lor \neg \left(t \leq 3.2 \cdot 10^{-104}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= t -7e-68) (not (<= t 3.2e-104)))
   (fma (* -27.0 j) k (fma (fma (* (* z y) x) 18.0 (* -4.0 a)) t (* c b)))
   (fma (* i x) -4.0 (fma c b (* (* j k) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((t <= -7e-68) || !(t <= 3.2e-104)) {
		tmp = fma((-27.0 * j), k, fma(fma(((z * y) * x), 18.0, (-4.0 * a)), t, (c * b)));
	} else {
		tmp = fma((i * x), -4.0, fma(c, b, ((j * k) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 ((t <= -7e-68) || !(t <= 3.2e-104))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)), t, Float64(c * b)));
	else
		tmp = fma(Float64(i * x), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[Or[LessEqual[t, -7e-68], N[Not[LessEqual[t, 3.2e-104]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000026e-68 or 3.19999999999999989e-104 < t

   1. Initial program 81.7%

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

   4. Applied rewrites 88.6%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 86.8

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

   6. Applied rewrites 86.8%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 80.4%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. lift-fma.f64 N/A

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

       5. lift-*.f64 N/A

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

       6. lift-fma.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. lift-*.f64 N/A

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

       9. *-commutative N/A

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

       10. associate-*r* N/A

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

   11. Applied rewrites 82.9%

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

   if -7.00000000000000026e-68 < t < 3.19999999999999989e-104

   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. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate--r+ N/A

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

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

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate--l+ N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. lower-fma.f64 N/A

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

   7. Applied rewrites 80.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 81.2

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

   9. Applied rewrites 81.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-68} \lor \neg \left(t \leq 3.2 \cdot 10^{-104}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-67} \lor \neg \left(t \leq 3.2 \cdot 10^{-104}\right):\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right), t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= t -2.4e-67) (not (<= t 3.2e-104)))
   (fma -27.0 (* j k) (fma (fma (* (* y z) x) 18.0 (* a -4.0)) t (* b c)))
   (fma (* i x) -4.0 (fma c b (* (* j k) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((t <= -2.4e-67) || !(t <= 3.2e-104)) {
		tmp = fma(-27.0, (j * k), fma(fma(((y * z) * x), 18.0, (a * -4.0)), t, (b * c)));
	} else {
		tmp = fma((i * x), -4.0, fma(c, b, ((j * k) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 ((t <= -2.4e-67) || !(t <= 3.2e-104))
		tmp = fma(-27.0, Float64(j * k), fma(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)), t, Float64(b * c)));
	else
		tmp = fma(Float64(i * x), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[Or[LessEqual[t, -2.4e-67], N[Not[LessEqual[t, 3.2e-104]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e-67 or 3.19999999999999989e-104 < t

   1. Initial program 81.7%

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

   4. Applied rewrites 88.6%

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

   5. Taylor expanded in i around 0

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

   7. Applied rewrites 80.4%

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

   if -2.4e-67 < t < 3.19999999999999989e-104

   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. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 80.2

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

   5. Applied rewrites 80.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate--r+ N/A

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

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

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate--l+ N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. lower-fma.f64 N/A

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

   7. Applied rewrites 80.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 81.2

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

   9. Applied rewrites 81.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-67} \lor \neg \left(t \leq 3.2 \cdot 10^{-104}\right):\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right), t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot t, i \cdot 4\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

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 -7.5e-18)
   (* (fma -18.0 (* (* z y) t) (* i 4.0)) (- x))
   (if (<= x 3.6e+110)
     (fma (* j k) -27.0 (fma (fma (* (* y x) 18.0) z (* -4.0 a)) t (* b c)))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) 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 <= -7.5e-18) {
		tmp = fma(-18.0, ((z * y) * t), (i * 4.0)) * -x;
	} else if (x <= 3.6e+110) {
		tmp = fma((j * k), -27.0, fma(fma(((y * x) * 18.0), z, (-4.0 * a)), t, (b * c)));
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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-18)
		tmp = Float64(fma(-18.0, Float64(Float64(z * y) * t), Float64(i * 4.0)) * Float64(-x));
	elseif (x <= 3.6e+110)
		tmp = fma(Float64(j * k), -27.0, fma(fma(Float64(Float64(y * x) * 18.0), z, Float64(-4.0 * a)), t, Float64(b * c)));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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-18], N[(N[(-18.0 * N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] + N[(i * 4.0), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[x, 3.6e+110], N[(N[(j * k), $MachinePrecision] * -27.0 + N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000015e-18

   1. Initial program 72.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   4. 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 72.6

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

   5. Applied rewrites 72.6%

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

   if -7.50000000000000015e-18 < x < 3.5999999999999997e110

   1. Initial program 90.4%

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

   4. Applied rewrites 89.2%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 92.5

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

   6. Applied rewrites 92.5%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 84.7%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. lower-fma.f64 N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. *-commutative N/A

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

       10. associate-*l* N/A

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

       11. *-commutative N/A

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

       12. associate-*r* N/A

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

       13. lower-fma.f64 N/A

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

       14. *-commutative N/A

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

       15. lower-*.f64 N/A

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

       16. *-commutative N/A

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

       17. lower-*.f64 N/A

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

       18. lift-*.f64 88.0

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

   11. Applied rewrites 88.0%

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

   if 3.5999999999999997e110 < x

   1. Initial program 65.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 81.3

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

   5. Applied rewrites 81.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot t, i \cdot 4\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot k, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right), t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+84} \lor \neg \left(t \leq 4.9 \cdot 10^{-104}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= t -1.5e+84) (not (<= t 4.9e-104)))
   (fma (fma (* (* z y) x) 18.0 (* -4.0 a)) t (* c b))
   (fma (* i x) -4.0 (fma c b (* (* j k) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((t <= -1.5e+84) || !(t <= 4.9e-104)) {
		tmp = fma(fma(((z * y) * x), 18.0, (-4.0 * a)), t, (c * b));
	} else {
		tmp = fma((i * x), -4.0, fma(c, b, ((j * k) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 ((t <= -1.5e+84) || !(t <= 4.9e-104))
		tmp = fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)), t, Float64(c * b));
	else
		tmp = fma(Float64(i * x), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[Or[LessEqual[t, -1.5e+84], N[Not[LessEqual[t, 4.9e-104]], $MachinePrecision]], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999998e84 or 4.9000000000000003e-104 < t

   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. Add Preprocessing

   4. Applied rewrites 87.5%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. associate-*r* N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 85.4

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

   6. Applied rewrites 85.4%

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

   7. Taylor expanded in i around 0

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

   9. Applied rewrites 79.8%

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

   10. Taylor expanded in j around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. +-commutative N/A

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

       10. lift-fma.f64 N/A

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

       11. lift-*.f64 N/A

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

       12. *-commutative N/A

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

       13. lower-*.f64 73.9

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

   12. Applied rewrites 73.9%

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

   if -1.49999999999999998e84 < t < 4.9000000000000003e-104

   1. Initial program 83.2%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 77.7

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

   5. Applied rewrites 77.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate--r+ N/A

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

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

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. associate--l+ N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. lower-fma.f64 N/A

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

   7. Applied rewrites 77.7%

      \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]

      3. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, -27 \cdot \left(j \cdot k\right) + b \cdot c\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + -27 \cdot \left(j \cdot k\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, c \cdot b + -27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]

      9. lift-*.f64 78.5

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]

   9. Applied rewrites 78.5%

      \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+84} \lor \neg \left(t \leq 4.9 \cdot 10^{-104}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+202}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+79}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+146}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

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+202)
   (* c b)
   (if (<= (* b c) -2e+79)
     (* -4.0 (* a t))
     (if (<= (* b c) 1e+146) (* -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+202) {
		tmp = c * b;
	} else if ((b * c) <= -2e+79) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 1e+146) {
		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+202)) then
        tmp = c * b
    else if ((b * c) <= (-2d+79)) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 1d+146) 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+202) {
		tmp = c * b;
	} else if ((b * c) <= -2e+79) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 1e+146) {
		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+202:
		tmp = c * b
	elif (b * c) <= -2e+79:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 1e+146:
		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+202)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -2e+79)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 1e+146)
		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+202)
		tmp = c * b;
	elseif ((b * c) <= -2e+79)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 1e+146)
		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+202], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e+79], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+146], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -9.999999999999999e201 or 9.99999999999999934e145 < (*.f64 b c)

   1. Initial program 77.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 69.0

         \[\leadsto c \cdot \color{blue}{b} \]

   5. Applied rewrites 69.0%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -9.999999999999999e201 < (*.f64 b c) < -1.99999999999999993e79

   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. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 44.3

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   5. Applied rewrites 44.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if -1.99999999999999993e79 < (*.f64 b c) < 9.99999999999999934e145

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. 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 27.7

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   5. Applied rewrites 27.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 54.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+146}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \left(j \cdot k\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \end{array} \end{array} \]

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) -5e+181)
   (fma -27.0 (* j k) (* b c))
   (if (<= (* b c) 1e+146)
     (fma (* i x) -4.0 (* (* j k) -27.0))
     (fma (* i -4.0) x (* b c)))))

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) <= -5e+181) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else if ((b * c) <= 1e+146) {
		tmp = fma((i * x), -4.0, ((j * k) * -27.0));
	} else {
		tmp = fma((i * -4.0), x, (b * c));
	}
	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) <= -5e+181)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	elseif (Float64(b * c) <= 1e+146)
		tmp = fma(Float64(i * x), -4.0, Float64(Float64(j * k) * -27.0));
	else
		tmp = fma(Float64(i * -4.0), x, Float64(b * c));
	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], -5e+181], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+146], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.0000000000000003e181

   1. Initial program 81.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 73.7

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -27 \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot k\right) + b \cdot \color{blue}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      6. lift-*.f64 71.5

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   8. Applied rewrites 71.5%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if -5.0000000000000003e181 < (*.f64 b c) < 9.99999999999999934e145

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 56.8

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 56.8%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto c \cdot b - \color{blue}{\mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(\color{blue}{i \cdot x}, 4, \left(k \cdot j\right) \cdot 27\right) \]

      3. *-commutative N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(\color{blue}{i \cdot x}, 4, \left(k \cdot j\right) \cdot 27\right) \]

      4. lift-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      5. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{\left(k \cdot j\right) \cdot 27}\right) \]

      6. *-commutative N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(k \cdot j\right)} \cdot 27\right) \]

      7. lift-*.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(k \cdot j\right) \cdot 27\right) \]

      8. *-commutative N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot k\right) \cdot 27\right) \]

      9. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot k\right) \cdot \color{blue}{27}\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

      11. associate--r+ N/A

          \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      12. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) - \color{blue}{27} \cdot \left(j \cdot k\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      14. +-commutative N/A

          \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - \color{blue}{27} \cdot \left(j \cdot k\right) \]

      15. associate--l+ N/A

          \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{\left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      16. *-commutative N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(\color{blue}{b \cdot c} - 27 \cdot \left(j \cdot k\right)\right) \]

      17. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(b \cdot c + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      18. metadata-eval N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(b \cdot c + -27 \cdot \left(\color{blue}{j} \cdot k\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(-27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c}\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, -27 \cdot \left(j \cdot k\right) + b \cdot c\right) \]

   7. Applied rewrites 56.8%

      \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{fma}\left(i \cdot x, -4, -27 \cdot \left(j \cdot k\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \left(j \cdot k\right) \cdot -27\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \left(j \cdot k\right) \cdot -27\right) \]

      3. lift-*.f64 51.8

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \left(j \cdot k\right) \cdot -27\right) \]

   10. Applied rewrites 51.8%

       \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \left(j \cdot k\right) \cdot -27\right) \]

   if 9.99999999999999934e145 < (*.f64 b c)

   1. Initial program 74.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 70.5

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 70.5%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(i \cdot x\right) \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \left(i \cdot x\right) + b \cdot \color{blue}{c} \]

      4. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot x + b \cdot c \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      8. lift-*.f64 72.8

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

   8. Applied rewrites 72.8%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, b \cdot c\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 72.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+125} \lor \neg \left(t \leq 3.6 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= t -2.85e+125) (not (<= t 3.6e+69)))
   (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)
   (fma (* i x) -4.0 (fma c b (* (* j k) -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((t <= -2.85e+125) || !(t <= 3.6e+69)) {
		tmp = fma(((z * y) * x), 18.0, (-4.0 * a)) * t;
	} else {
		tmp = fma((i * x), -4.0, fma(c, b, ((j * k) * -27.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 ((t <= -2.85e+125) || !(t <= 3.6e+69))
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * t);
	else
		tmp = fma(Float64(i * x), -4.0, fma(c, b, Float64(Float64(j * k) * -27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[Or[LessEqual[t, -2.85e+125], N[Not[LessEqual[t, 3.6e+69]], $MachinePrecision]], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b + N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8499999999999998e125 or 3.6000000000000003e69 < t

   1. Initial program 77.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. 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. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      11. lower-*.f64 71.3

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

   5. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]

   if -2.8499999999999998e125 < t < 3.6000000000000003e69

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 73.7

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto c \cdot b - \color{blue}{\mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(\color{blue}{i \cdot x}, 4, \left(k \cdot j\right) \cdot 27\right) \]

      3. *-commutative N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(\color{blue}{i \cdot x}, 4, \left(k \cdot j\right) \cdot 27\right) \]

      4. lift-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      5. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{\left(k \cdot j\right) \cdot 27}\right) \]

      6. *-commutative N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(k \cdot j\right)} \cdot 27\right) \]

      7. lift-*.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(k \cdot j\right) \cdot 27\right) \]

      8. *-commutative N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot k\right) \cdot 27\right) \]

      9. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot k\right) \cdot \color{blue}{27}\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

      11. associate--r+ N/A

          \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      12. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) - \color{blue}{27} \cdot \left(j \cdot k\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      14. +-commutative N/A

          \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - \color{blue}{27} \cdot \left(j \cdot k\right) \]

      15. associate--l+ N/A

          \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{\left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      16. *-commutative N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(\color{blue}{b \cdot c} - 27 \cdot \left(j \cdot k\right)\right) \]

      17. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(b \cdot c + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      18. metadata-eval N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(b \cdot c + -27 \cdot \left(\color{blue}{j} \cdot k\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(-27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c}\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, -27 \cdot \left(j \cdot k\right) + b \cdot c\right) \]

   7. Applied rewrites 73.6%

      \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]

      3. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, -27 \cdot \left(j \cdot k\right) + b \cdot c\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, b \cdot c + -27 \cdot \left(j \cdot k\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, c \cdot b + -27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, -27 \cdot \left(j \cdot k\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]

      9. lift-*.f64 74.3

         \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]

   9. Applied rewrites 74.3%

      \[\leadsto \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+125} \lor \neg \left(t \leq 3.6 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(c, b, \left(j \cdot k\right) \cdot -27\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+125} \lor \neg \left(t \leq 3.6 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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 (or (<= t -2.85e+125) (not (<= t 3.6e+69)))
   (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)
   (fma (* i x) -4.0 (fma -27.0 (* j k) (* b c)))))

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 ((t <= -2.85e+125) || !(t <= 3.6e+69)) {
		tmp = fma(((z * y) * x), 18.0, (-4.0 * a)) * t;
	} else {
		tmp = fma((i * x), -4.0, fma(-27.0, (j * k), (b * c)));
	}
	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 ((t <= -2.85e+125) || !(t <= 3.6e+69))
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * t);
	else
		tmp = fma(Float64(i * x), -4.0, fma(-27.0, Float64(j * k), Float64(b * c)));
	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[Or[LessEqual[t, -2.85e+125], N[Not[LessEqual[t, 3.6e+69]], $MachinePrecision]], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8499999999999998e125 or 3.6000000000000003e69 < t

   1. Initial program 77.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   4. 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. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      11. lower-*.f64 71.3

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

   5. Applied rewrites 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]

   if -2.8499999999999998e125 < t < 3.6000000000000003e69

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 73.7

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto c \cdot b - \color{blue}{\mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(\color{blue}{i \cdot x}, 4, \left(k \cdot j\right) \cdot 27\right) \]

      3. *-commutative N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(\color{blue}{i \cdot x}, 4, \left(k \cdot j\right) \cdot 27\right) \]

      4. lift-*.f64 N/A

         \[\leadsto b \cdot c - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      5. lift-fma.f64 N/A

         \[\leadsto b \cdot c - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{\left(k \cdot j\right) \cdot 27}\right) \]

      6. *-commutative N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \color{blue}{\left(k \cdot j\right)} \cdot 27\right) \]

      7. lift-*.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(k \cdot j\right) \cdot 27\right) \]

      8. *-commutative N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot k\right) \cdot 27\right) \]

      9. lower-*.f64 N/A

         \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + \left(j \cdot k\right) \cdot \color{blue}{27}\right) \]

      10. *-commutative N/A

          \[\leadsto b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \color{blue}{\left(j \cdot k\right)}\right) \]

      11. associate--r+ N/A

          \[\leadsto \left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]

      12. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right) - \color{blue}{27} \cdot \left(j \cdot k\right) \]

      13. metadata-eval N/A

          \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      14. +-commutative N/A

          \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right) - \color{blue}{27} \cdot \left(j \cdot k\right) \]

      15. associate--l+ N/A

          \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{\left(b \cdot c - 27 \cdot \left(j \cdot k\right)\right)} \]

      16. *-commutative N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(\color{blue}{b \cdot c} - 27 \cdot \left(j \cdot k\right)\right) \]

      17. fp-cancel-sub-sign-inv N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(b \cdot c + \color{blue}{\left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)}\right) \]

      18. metadata-eval N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(b \cdot c + -27 \cdot \left(\color{blue}{j} \cdot k\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \left(i \cdot x\right) \cdot -4 + \left(-27 \cdot \left(j \cdot k\right) + \color{blue}{b \cdot c}\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, -27 \cdot \left(j \cdot k\right) + b \cdot c\right) \]

   7. Applied rewrites 73.6%

      \[\leadsto \mathsf{fma}\left(i \cdot x, \color{blue}{-4}, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+125} \lor \neg \left(t \leq 3.6 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-21} \lor \neg \left(x \leq 1.05 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \end{array} \end{array} \]

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 (or (<= x -1.5e-21) (not (<= x 1.05e+96)))
   (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
   (fma -27.0 (* j k) (* b c))))

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 <= -1.5e-21) || !(x <= 1.05e+96)) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else {
		tmp = fma(-27.0, (j * k), (b * c));
	}
	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 <= -1.5e-21) || !(x <= 1.05e+96))
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	else
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	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[Or[LessEqual[x, -1.5e-21], N[Not[LessEqual[x, 1.05e+96]], $MachinePrecision]], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999996e-21 or 1.0500000000000001e96 < x

   1. Initial program 69.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + -4 \cdot i\right) \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 75.2

          \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

   5. Applied rewrites 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x} \]

   if -1.49999999999999996e-21 < x < 1.0500000000000001e96

   1. Initial program 90.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 67.2

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 67.2%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -27 \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot k\right) + b \cdot \color{blue}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      6. lift-*.f64 61.0

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   8. Applied rewrites 61.0%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-21} \lor \neg \left(x \leq 1.05 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \mathbf{if}\;x \leq -3.65 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right) \cdot 18\\ \end{array} \end{array} \]

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
 (let* ((t_1 (fma (* i -4.0) x (* b c))))
   (if (<= x -3.65e-22)
     t_1
     (if (<= x 4.6e-47)
       (fma -27.0 (* j k) (* b c))
       (if (<= x 9e+159) t_1 (* (* (* 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 t_1 = fma((i * -4.0), x, (b * c));
	double tmp;
	if (x <= -3.65e-22) {
		tmp = t_1;
	} else if (x <= 4.6e-47) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else if (x <= 9e+159) {
		tmp = t_1;
	} 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)
	t_1 = fma(Float64(i * -4.0), x, Float64(b * c))
	tmp = 0.0
	if (x <= -3.65e-22)
		tmp = t_1;
	elseif (x <= 4.6e-47)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	elseif (x <= 9e+159)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y * x) * Float64(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_] := Block[{t$95$1 = N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.65e-22], t$95$1, If[LessEqual[x, 4.6e-47], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+159], t$95$1, N[(N[(N[(y * x), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.65000000000000014e-22 or 4.59999999999999964e-47 < x < 9.00000000000000053e159

   1. Initial program 74.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 58.2

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 58.2%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(i \cdot x\right) \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \left(i \cdot x\right) + b \cdot \color{blue}{c} \]

      4. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot x + b \cdot c \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      8. lift-*.f64 52.4

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

   8. Applied rewrites 52.4%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, b \cdot c\right) \]

   if -3.65000000000000014e-22 < x < 4.59999999999999964e-47

   1. Initial program 92.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 68.2

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 68.2%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -27 \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot k\right) + b \cdot \color{blue}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      6. lift-*.f64 64.5

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   8. Applied rewrites 64.5%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if 9.00000000000000053e159 < x

   1. Initial program 63.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. 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. *-commutative N/A

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      7. *-commutative N/A

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      8. lower-*.f64 64.2

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(z \cdot y\right)\right) \cdot t\right) \cdot 18 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(x \cdot \left(z \cdot y\right)\right) \cdot t\right) \cdot 18 \]

      4. *-commutative 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. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      7. lower-*.f64 64.1

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

   7. Applied rewrites 64.1%

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      4. associate-*l* N/A

         \[\leadsto \left(\left(x \cdot y\right) \cdot \left(z \cdot t\right)\right) \cdot 18 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\left(x \cdot y\right) \cdot \left(z \cdot t\right)\right) \cdot 18 \]

      6. *-commutative N/A

         \[\leadsto \left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right) \cdot 18 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right) \cdot 18 \]

      8. lower-*.f64 64.1

         \[\leadsto \left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right) \cdot 18 \]

   9. Applied rewrites 64.1%

      \[\leadsto \left(\left(y \cdot x\right) \cdot \left(z \cdot t\right)\right) \cdot 18 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 37.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+199} \lor \neg \left(b \cdot c \leq 10^{+146}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

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 (or (<= (* b c) -5e+199) (not (<= (* b c) 1e+146)))
   (* c b)
   (* -27.0 (* k j))))

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) <= -5e+199) || !((b * c) <= 1e+146)) {
		tmp = c * b;
	} else {
		tmp = -27.0 * (k * j);
	}
	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) <= (-5d+199)) .or. (.not. ((b * c) <= 1d+146))) then
        tmp = c * b
    else
        tmp = (-27.0d0) * (k * j)
    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) <= -5e+199) || !((b * c) <= 1e+146)) {
		tmp = c * b;
	} else {
		tmp = -27.0 * (k * j);
	}
	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) <= -5e+199) or not ((b * c) <= 1e+146):
		tmp = c * b
	else:
		tmp = -27.0 * (k * j)
	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) <= -5e+199) || !(Float64(b * c) <= 1e+146))
		tmp = Float64(c * b);
	else
		tmp = Float64(-27.0 * Float64(k * j));
	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) <= -5e+199) || ~(((b * c) <= 1e+146)))
		tmp = c * b;
	else
		tmp = -27.0 * (k * j);
	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[Or[LessEqual[N[(b * c), $MachinePrecision], -5e+199], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+146]], $MachinePrecision]], N[(c * b), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.9999999999999998e199 or 9.99999999999999934e145 < (*.f64 b c)

   1. Initial program 78.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 67.5

         \[\leadsto c \cdot \color{blue}{b} \]

   5. Applied rewrites 67.5%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.9999999999999998e199 < (*.f64 b c) < 9.99999999999999934e145

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. 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 26.2

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   5. Applied rewrites 26.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+199} \lor \neg \left(b \cdot c \leq 10^{+146}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) \cdot 18\\ \end{array} \end{array} \]

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 -3.65e-22)
   (fma (* i -4.0) x (* b c))
   (if (<= x 3.5e+96)
     (fma -27.0 (* j k) (* b c))
     (* (* (* y z) (* x 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 <= -3.65e-22) {
		tmp = fma((i * -4.0), x, (b * c));
	} else if (x <= 3.5e+96) {
		tmp = fma(-27.0, (j * k), (b * c));
	} else {
		tmp = ((y * z) * (x * 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 <= -3.65e-22)
		tmp = fma(Float64(i * -4.0), x, Float64(b * c));
	elseif (x <= 3.5e+96)
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	else
		tmp = Float64(Float64(Float64(y * z) * Float64(x * 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, -3.65e-22], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+96], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision] * 18.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.65000000000000014e-22

   1. Initial program 72.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 53.9

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 53.9%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(i \cdot x\right) \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \left(i \cdot x\right) + b \cdot \color{blue}{c} \]

      4. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot x + b \cdot c \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      8. lift-*.f64 50.9

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

   8. Applied rewrites 50.9%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, b \cdot c\right) \]

   if -3.65000000000000014e-22 < x < 3.4999999999999999e96

   1. Initial program 90.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 67.2

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 67.2%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -27 \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot k\right) + b \cdot \color{blue}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      6. lift-*.f64 61.0

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   8. Applied rewrites 61.0%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]

   if 3.4999999999999999e96 < x

   1. Initial program 65.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   4. 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. *-commutative N/A

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      7. *-commutative N/A

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      8. lower-*.f64 53.0

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

   5. Applied rewrites 53.0%

      \[\leadsto \color{blue}{\left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t\right) \cdot 18 \]

      3. associate-*l* N/A

         \[\leadsto \left(\left(z \cdot y\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(z \cdot y\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]

      8. lower-*.f64 59.9

         \[\leadsto \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]

   7. Applied rewrites 59.9%

      \[\leadsto \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right) \cdot 18 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 50.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{-22} \lor \neg \left(x \leq 4.6 \cdot 10^{-47}\right):\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \end{array} \end{array} \]

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 (or (<= x -3.65e-22) (not (<= x 4.6e-47)))
   (fma (* i -4.0) x (* b c))
   (fma -27.0 (* j k) (* b c))))

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 <= -3.65e-22) || !(x <= 4.6e-47)) {
		tmp = fma((i * -4.0), x, (b * c));
	} else {
		tmp = fma(-27.0, (j * k), (b * c));
	}
	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 <= -3.65e-22) || !(x <= 4.6e-47))
		tmp = fma(Float64(i * -4.0), x, Float64(b * c));
	else
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	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[Or[LessEqual[x, -3.65e-22], N[Not[LessEqual[x, 4.6e-47]], $MachinePrecision]], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.65000000000000014e-22 or 4.59999999999999964e-47 < x

   1. Initial program 73.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 57.0

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 57.0%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(i \cdot x\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -4 \cdot \left(i \cdot x\right) \]

      3. +-commutative N/A

         \[\leadsto -4 \cdot \left(i \cdot x\right) + b \cdot \color{blue}{c} \]

      4. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot x + b \cdot c \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      8. lift-*.f64 50.9

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

   8. Applied rewrites 50.9%

      \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, b \cdot c\right) \]

   if -3.65000000000000014e-22 < x < 4.59999999999999964e-47

   1. Initial program 92.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 68.2

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 68.2%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -27 \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot k\right) + b \cdot \color{blue}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      6. lift-*.f64 64.5

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   8. Applied rewrites 64.5%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{-22} \lor \neg \left(x \leq 4.6 \cdot 10^{-47}\right):\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 45.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-18} \lor \neg \left(x \leq 2.4 \cdot 10^{+107}\right):\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \end{array} \end{array} \]

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 (or (<= x -7.5e-18) (not (<= x 2.4e+107)))
   (* (* -4.0 i) x)
   (fma -27.0 (* j k) (* b c))))

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-18) || !(x <= 2.4e+107)) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = fma(-27.0, (j * k), (b * c));
	}
	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-18) || !(x <= 2.4e+107))
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = fma(-27.0, Float64(j * k), Float64(b * c));
	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[Or[LessEqual[x, -7.5e-18], N[Not[LessEqual[x, 2.4e+107]], $MachinePrecision]], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000015e-18 or 2.4000000000000001e107 < x

   1. Initial program 69.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 41.5

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   5. Applied rewrites 41.5%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

   if -7.50000000000000015e-18 < x < 2.4000000000000001e107

   1. Initial program 90.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(i \cdot x\right)} + 27 \cdot \left(j \cdot k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto c \cdot b - \left(\left(i \cdot x\right) \cdot 4 + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, \color{blue}{4}, 27 \cdot \left(j \cdot k\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, 27 \cdot \left(j \cdot k\right)\right) \]

      7. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(j \cdot k\right) \cdot 27\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

      10. lower-*.f64 66.6

          \[\leadsto c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right) \]

   5. Applied rewrites 66.6%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto b \cdot c - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   7. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(27\right)\right) \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. metadata-eval N/A

         \[\leadsto b \cdot c + -27 \cdot \left(j \cdot k\right) \]

      3. +-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot k\right) + b \cdot \color{blue}{c} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot \color{blue}{k}, b \cdot c\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

      6. lift-*.f64 60.4

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right) \]

   8. Applied rewrites 60.4%

      \[\leadsto \mathsf{fma}\left(-27, \color{blue}{j \cdot k}, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-18} \lor \neg \left(x \leq 2.4 \cdot 10^{+107}\right):\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 23.7% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

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 81.5%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto c \cdot \color{blue}{b} \]

   2. lower-*.f64 26.2

      \[\leadsto c \cdot \color{blue}{b} \]

5. Applied rewrites 26.2%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

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 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025064 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))