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

Percentage Accurate: 85.4% → 91.3%

Time: 6.8s

Alternatives: 18

Speedup: 1.0×

• 50.9% 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: 85.4% 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: 91.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{+294}:\\ \;\;\;\;t\_1 - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(-\mathsf{fma}\left(-18 \cdot t, z \cdot x, -\frac{c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)}{y}\right) \cdot y\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

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
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 4e+294)
     (- t_1 (* j (* k 27.0)))
     (if (<= t_1 INFINITY)
       (-
        (-
         (*
          (fma
           (* -18.0 t)
           (* z x)
           (- (/ (- (* c b) (* 4.0 (fma a t (* i x)))) y)))
          y))
        (* (* j 27.0) k))
       (fma
        (* k j)
        -27.0
        (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* 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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 4e+294) {
		tmp = t_1 - (j * (k * 27.0));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = -(fma((-18.0 * t), (z * x), -(((c * b) - (4.0 * fma(a, t, (i * x)))) / y)) * y) - ((j * 27.0) * k);
	} else {
		tmp = fma((k * j), -27.0, fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (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(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))
	tmp = 0.0
	if (t_1 <= 4e+294)
		tmp = Float64(t_1 - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(-Float64(fma(Float64(-18.0 * t), Float64(z * x), Float64(-Float64(Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))) / y))) * y)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(k * j), -27.0, fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, 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[(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]}, If[LessEqual[t$95$1, 4e+294], N[(t$95$1 - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[((-N[(N[(N[(-18.0 * t), $MachinePrecision] * N[(z * x), $MachinePrecision] + (-N[(N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision])), $MachinePrecision] * y), $MachinePrecision]) - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 4.00000000000000027e294

   1. Initial program 85.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.4

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

   3. Applied rewrites 85.4%

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

   if 4.00000000000000027e294 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < +inf.0

   1. Initial program 85.4%

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

   2. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 76.8%

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

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

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   7. Applied rewrites 76.1%

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

Alternative 2: 90.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

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
 (if (<= x -4e+43)
   (-
    (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b))
    (fma (* k j) 27.0 (* (* a t) 4.0)))
   (if (<= x 1.05e+146)
     (-
      (-
       (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
       (* (* x 4.0) i))
      (* j (* k 27.0)))
     (fma (* k j) -27.0 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* 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 (x <= -4e+43) {
		tmp = fma(fma((18.0 * t), (z * y), (-4.0 * i)), x, (c * b)) - fma((k * j), 27.0, ((a * t) * 4.0));
	} else if (x <= 1.05e+146) {
		tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - (j * (k * 27.0));
	} else {
		tmp = fma((k * j), -27.0, fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (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 (x <= -4e+43)
		tmp = Float64(fma(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)), x, Float64(c * b)) - fma(Float64(k * j), 27.0, Float64(Float64(a * t) * 4.0)));
	elseif (x <= 1.05e+146)
		tmp = 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(j * Float64(k * 27.0)));
	else
		tmp = fma(Float64(k * j), -27.0, fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -4e+43], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+146], 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[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.00000000000000006e43

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   if -4.00000000000000006e43 < x < 1.05e146

   1. Initial program 85.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.4

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

   3. Applied rewrites 85.4%

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

   if 1.05e146 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   7. Applied rewrites 76.1%

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

Alternative 3: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(i \cdot x, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

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
 (if (<= x -9e-182)
   (-
    (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b))
    (fma (* k j) 27.0 (* (* a t) 4.0)))
   (if (<= x 7.1e+34)
     (fma (* -4.0 a) t (- (fma (* i x) -4.0 (* c b)) (* (* k j) 27.0)))
     (fma (* k j) -27.0 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* 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 (x <= -9e-182) {
		tmp = fma(fma((18.0 * t), (z * y), (-4.0 * i)), x, (c * b)) - fma((k * j), 27.0, ((a * t) * 4.0));
	} else if (x <= 7.1e+34) {
		tmp = fma((-4.0 * a), t, (fma((i * x), -4.0, (c * b)) - ((k * j) * 27.0)));
	} else {
		tmp = fma((k * j), -27.0, fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (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 (x <= -9e-182)
		tmp = Float64(fma(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)), x, Float64(c * b)) - fma(Float64(k * j), 27.0, Float64(Float64(a * t) * 4.0)));
	elseif (x <= 7.1e+34)
		tmp = fma(Float64(-4.0 * a), t, Float64(fma(Float64(i * x), -4.0, Float64(c * b)) - Float64(Float64(k * j) * 27.0)));
	else
		tmp = fma(Float64(k * j), -27.0, fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -9e-182], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.1e+34], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.9999999999999998e-182

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   if -8.9999999999999998e-182 < x < 7.09999999999999956e34

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. associate--r+ N/A

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

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

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

   6. Applied rewrites 77.2%

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

   if 7.09999999999999956e34 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   7. Applied rewrites 76.1%

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

Alternative 4: 86.9% accurate, 0.6× speedup

Math

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

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
 (if (<=
      (-
       (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
       (* (* x 4.0) i))
      INFINITY)
   (fma
    (* -27.0 j)
    k
    (fma (* 18.0 t) (* (* z y) x) (- (* c b) (* 4.0 (fma a t (* i x))))))
   (fma (* k j) -27.0 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* 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 ((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) <= ((double) INFINITY)) {
		tmp = fma((-27.0 * j), k, fma((18.0 * t), ((z * y) * x), ((c * b) - (4.0 * fma(a, t, (i * x))))));
	} else {
		tmp = fma((k * j), -27.0, fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (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(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) <= Inf)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(18.0 * t), Float64(Float64(z * y) * x), Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x))))));
	else
		tmp = fma(Float64(k * j), -27.0, fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b)));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.4%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 87.5%

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

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

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   7. Applied rewrites 76.1%

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

Alternative 5: 83.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(i \cdot x, -4, c \cdot b\right) - \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* k j)
          -27.0
          (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b)))))
   (if (<= x -1.02e+152)
     t_1
     (if (<= x 7.1e+34)
       (fma (* -4.0 a) t (- (fma (* i x) -4.0 (* c b)) (* (* k j) 27.0)))
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((k * j), -27.0, fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b)));
	double tmp;
	if (x <= -1.02e+152) {
		tmp = t_1;
	} else if (x <= 7.1e+34) {
		tmp = fma((-4.0 * a), t, (fma((i * x), -4.0, (c * b)) - ((k * j) * 27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * j), -27.0, fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b)))
	tmp = 0.0
	if (x <= -1.02e+152)
		tmp = t_1;
	elseif (x <= 7.1e+34)
		tmp = fma(Float64(-4.0 * a), t, Float64(fma(Float64(i * x), -4.0, Float64(c * b)) - Float64(Float64(k * j) * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+152], t$95$1, If[LessEqual[x, 7.1e+34], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999999e152 or 7.09999999999999956e34 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

   7. Applied rewrites 76.1%

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

   if -1.01999999999999999e152 < x < 7.09999999999999956e34

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. associate--r+ N/A

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

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

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

   6. Applied rewrites 77.2%

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

Alternative 6: 79.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+263}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-27, k \cdot j, c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(18 \cdot x\right) \cdot y, z, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= z -4.5e+28)
   (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
   (if (<= z 1.75e+263)
     (fma (* -4.0 a) t (fma (* -4.0 i) x (fma -27.0 (* k j) (* c b))))
     (* (fma (* (* 18.0 x) y) z (* -4.0 a)) t))))

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 (z <= -4.5e+28) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else if (z <= 1.75e+263) {
		tmp = fma((-4.0 * a), t, fma((-4.0 * i), x, fma(-27.0, (k * j), (c * b))));
	} else {
		tmp = fma(((18.0 * x) * y), z, (-4.0 * a)) * t;
	}
	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 (z <= -4.5e+28)
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	elseif (z <= 1.75e+263)
		tmp = fma(Float64(-4.0 * a), t, fma(Float64(-4.0 * i), x, fma(-27.0, Float64(k * j), Float64(c * b))));
	else
		tmp = Float64(fma(Float64(Float64(18.0 * x) * y), z, Float64(-4.0 * a)) * t);
	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[z, -4.5e+28], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.75e+263], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(-4.0 * i), $MachinePrecision] * x + N[(-27.0 * N[(k * j), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999997e28

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. 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 43.0

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

   4. Applied rewrites 43.0%

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

   if -4.4999999999999997e28 < z < 1.74999999999999999e263

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. associate--r+ N/A

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

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

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

   6. Applied rewrites 77.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate--l+ N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

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

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lower-fma.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. *-commutative N/A

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

      22. lift-*.f64 78.0

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

   8. Applied rewrites 78.0%

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

   if 1.74999999999999999e263 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. 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. fp-cancel-sub-sign-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 43.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 43.7

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

   9. Applied rewrites 43.7%

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

Alternative 7: 78.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+263}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(18 \cdot x\right) \cdot y, z, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= z -3.6e+27)
   (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
   (if (<= z 1.75e+263)
     (- (* c b) (fma 4.0 (fma a t (* i x)) (* (* k j) 27.0)))
     (* (fma (* (* 18.0 x) y) z (* -4.0 a)) t))))

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 (z <= -3.6e+27) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else if (z <= 1.75e+263) {
		tmp = (c * b) - fma(4.0, fma(a, t, (i * x)), ((k * j) * 27.0));
	} else {
		tmp = fma(((18.0 * x) * y), z, (-4.0 * a)) * t;
	}
	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 (z <= -3.6e+27)
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	elseif (z <= 1.75e+263)
		tmp = Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), Float64(Float64(k * j) * 27.0)));
	else
		tmp = Float64(fma(Float64(Float64(18.0 * x) * y), z, Float64(-4.0 * a)) * t);
	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[z, -3.6e+27], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.75e+263], N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999983e27

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. 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 43.0

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

   4. Applied rewrites 43.0%

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

   if -3.59999999999999983e27 < z < 1.74999999999999999e263

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   if 1.74999999999999999e263 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. 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. fp-cancel-sub-sign-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 43.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 43.7

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

   9. Applied rewrites 43.7%

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

Alternative 8: 72.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-15}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(18 \cdot x\right) \cdot y, z, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 (<= t -2.5e+18)
   (* (fma (* (* y x) 18.0) z (* -4.0 a)) t)
   (if (<= t 5e-15)
     (- (* c b) (fma (* i x) 4.0 (* (* k j) 27.0)))
     (if (<= t 1.08e+130)
       (fma c b (* -4.0 (fma i x (* a t))))
       (* (fma (* (* 18.0 x) y) z (* -4.0 a)) t)))))

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 <= -2.5e+18) {
		tmp = fma(((y * x) * 18.0), z, (-4.0 * a)) * t;
	} else if (t <= 5e-15) {
		tmp = (c * b) - fma((i * x), 4.0, ((k * j) * 27.0));
	} else if (t <= 1.08e+130) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t))));
	} else {
		tmp = fma(((18.0 * x) * y), z, (-4.0 * a)) * t;
	}
	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 <= -2.5e+18)
		tmp = Float64(fma(Float64(Float64(y * x) * 18.0), z, Float64(-4.0 * a)) * t);
	elseif (t <= 5e-15)
		tmp = Float64(Float64(c * b) - fma(Float64(i * x), 4.0, Float64(Float64(k * j) * 27.0)));
	elseif (t <= 1.08e+130)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))));
	else
		tmp = Float64(fma(Float64(Float64(18.0 * x) * y), z, Float64(-4.0 * a)) * t);
	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[t, -2.5e+18], N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 5e-15], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+130], N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.5e18

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. 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. fp-cancel-sub-sign-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 43.7%

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

   if -2.5e18 < t < 4.99999999999999999e-15

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-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 60.7

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

   4. Applied rewrites 60.7%

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

   if 4.99999999999999999e-15 < t < 1.08e130

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.0

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

   7. Applied rewrites 59.0%

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

   if 1.08e130 < t

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} \]
   6. 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. fp-cancel-sub-sign-inv N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 43.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 43.7

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

   9. Applied rewrites 43.7%

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

Alternative 9: 72.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(-27, k \cdot j, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)))
   (if (<= x -1.9e+131)
     t_1
     (if (<= x 6e+33) (fma (* -4.0 a) t (fma -27.0 (* k j) (* c b))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	double tmp;
	if (x <= -1.9e+131) {
		tmp = t_1;
	} else if (x <= 6e+33) {
		tmp = fma((-4.0 * a), t, fma(-27.0, (k * j), (c * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x)
	tmp = 0.0
	if (x <= -1.9e+131)
		tmp = t_1;
	elseif (x <= 6e+33)
		tmp = fma(Float64(-4.0 * a), t, fma(-27.0, Float64(k * j), Float64(c * b)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.9e+131], t$95$1, If[LessEqual[x, 6e+33], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(-27.0 * N[(k * j), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9000000000000002e131 or 5.99999999999999967e33 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. 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 43.0

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

   4. Applied rewrites 43.0%

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

   if -1.9000000000000002e131 < x < 5.99999999999999967e33

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. associate--r+ N/A

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

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

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

   6. Applied rewrites 77.2%

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

   7. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 61.9

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

   9. Applied rewrites 61.9%

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

Alternative 10: 64.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -2.9 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \left(k \cdot j\right) \cdot 27\\ \end{array} \end{array} \]

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 (<= k -2.9e+44)
   (fma (* -4.0 a) t (* (* k j) -27.0))
   (if (<= k 2.1e+152)
     (fma c b (* -4.0 (fma i x (* a t))))
     (- (* c b) (* (* k j) 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 (k <= -2.9e+44) {
		tmp = fma((-4.0 * a), t, ((k * j) * -27.0));
	} else if (k <= 2.1e+152) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t))));
	} else {
		tmp = (c * b) - ((k * j) * 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 (k <= -2.9e+44)
		tmp = fma(Float64(-4.0 * a), t, Float64(Float64(k * j) * -27.0));
	elseif (k <= 2.1e+152)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))));
	else
		tmp = Float64(Float64(c * b) - Float64(Float64(k * j) * 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[LessEqual[k, -2.9e+44], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e+152], N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.9000000000000002e44

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. associate--r+ N/A

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

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

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

   6. Applied rewrites 77.2%

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

   7. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 61.9

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

   9. Applied rewrites 61.9%

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

   10. Taylor expanded in b around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 42.8

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

   12. Applied rewrites 42.8%

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

   if -2.9000000000000002e44 < k < 2.1000000000000002e152

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.0

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

   7. Applied rewrites 59.0%

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

   if 2.1000000000000002e152 < k

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 41.5

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

   7. Applied rewrites 41.5%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

      3. lift-*.f64 41.6

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

   10. Applied rewrites 41.6%

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

   11. Taylor expanded in j around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 44.5

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

   13. Applied rewrites 44.5%

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

Alternative 11: 50.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.1 \cdot 10^{-89}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \left(k \cdot j\right) \cdot 27\\ \end{array} \end{array} \]

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 (<= k -3.1e-89)
   (fma (* -4.0 a) t (* (* k j) -27.0))
   (if (<= k 1.9e+64)
     (fma (* -4.0 a) t (* c b))
     (if (<= k 1.4e+152)
       (* (fma i x (* a t)) -4.0)
       (- (* c b) (* (* k j) 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 (k <= -3.1e-89) {
		tmp = fma((-4.0 * a), t, ((k * j) * -27.0));
	} else if (k <= 1.9e+64) {
		tmp = fma((-4.0 * a), t, (c * b));
	} else if (k <= 1.4e+152) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} else {
		tmp = (c * b) - ((k * j) * 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 (k <= -3.1e-89)
		tmp = fma(Float64(-4.0 * a), t, Float64(Float64(k * j) * -27.0));
	elseif (k <= 1.9e+64)
		tmp = fma(Float64(-4.0 * a), t, Float64(c * b));
	elseif (k <= 1.4e+152)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = Float64(Float64(c * b) - Float64(Float64(k * j) * 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[LessEqual[k, -3.1e-89], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.9e+64], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e+152], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.09999999999999996e-89

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. associate-+r+ N/A

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

      13. associate--r+ N/A

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

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

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

   6. Applied rewrites 77.2%

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

   7. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 61.9

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

   9. Applied rewrites 61.9%

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

   10. Taylor expanded in b around 0

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 42.8

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

   12. Applied rewrites 42.8%

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

   if -3.09999999999999996e-89 < k < 1.9000000000000001e64

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.0

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in x around 0

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

      1. associate-*l* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      2. lower-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 42.0

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

   10. Applied rewrites 42.0%

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

   if 1.9000000000000001e64 < k < 1.4000000000000001e152

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.0

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 39.6

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

   10. Applied rewrites 39.6%

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

   if 1.4000000000000001e152 < k

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 41.5

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

   7. Applied rewrites 41.5%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

      3. lift-*.f64 41.6

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

   10. Applied rewrites 41.6%

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

   11. Taylor expanded in j around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 44.5

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

   13. Applied rewrites 44.5%

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

Alternative 12: 50.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.65 \cdot 10^{+24}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \left(k \cdot j\right) \cdot 27\\ \end{array} \end{array} \]

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 (<= k -1.65e+24)
   (* (* -27.0 j) k)
   (if (<= k 1.9e+64)
     (fma (* -4.0 a) t (* c b))
     (if (<= k 1.4e+152)
       (* (fma i x (* a t)) -4.0)
       (- (* c b) (* (* k j) 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 (k <= -1.65e+24) {
		tmp = (-27.0 * j) * k;
	} else if (k <= 1.9e+64) {
		tmp = fma((-4.0 * a), t, (c * b));
	} else if (k <= 1.4e+152) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} else {
		tmp = (c * b) - ((k * j) * 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 (k <= -1.65e+24)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (k <= 1.9e+64)
		tmp = fma(Float64(-4.0 * a), t, Float64(c * b));
	elseif (k <= 1.4e+152)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = Float64(Float64(c * b) - Float64(Float64(k * j) * 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[LessEqual[k, -1.65e+24], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[k, 1.9e+64], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.4e+152], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.6499999999999999e24

   1. Initial program 85.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 24.4

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

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 24.4

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

   6. Applied rewrites 24.4%

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

   if -1.6499999999999999e24 < k < 1.9000000000000001e64

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.0

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in x around 0

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

      1. associate-*l* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      2. lower-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 42.0

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

   10. Applied rewrites 42.0%

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

   if 1.9000000000000001e64 < k < 1.4000000000000001e152

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-*.f64 59.0

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 39.6

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

   10. Applied rewrites 39.6%

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

   if 1.4000000000000001e152 < k

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 41.5

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

   7. Applied rewrites 41.5%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

      3. lift-*.f64 41.6

         \[\leadsto c \cdot b - \left(a \cdot t\right) \cdot 4 \]

   10. Applied rewrites 41.6%

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

   11. Taylor expanded in j around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 44.5

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

   13. Applied rewrites 44.5%

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

Alternative 13: 50.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.65 \cdot 10^{+24}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+154}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

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 (<= k -1.65e+24)
   (* (* -27.0 j) k)
   (if (<= k 1.9e+64)
     (fma (* -4.0 a) t (* c b))
     (if (<= k 4.5e+154) (* (fma i x (* a t)) -4.0) (* (* -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 (k <= -1.65e+24) {
		tmp = (-27.0 * j) * k;
	} else if (k <= 1.9e+64) {
		tmp = fma((-4.0 * a), t, (c * b));
	} else if (k <= 4.5e+154) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} 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 (k <= -1.65e+24)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (k <= 1.9e+64)
		tmp = fma(Float64(-4.0 * a), t, Float64(c * b));
	elseif (k <= 4.5e+154)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = Float64(Float64(-27.0 * k) * j);
	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[k, -1.65e+24], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[k, 1.9e+64], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.5e+154], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.6499999999999999e24

   1. Initial program 85.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 24.4

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

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 24.4

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

   6. Applied rewrites 24.4%

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

   if -1.6499999999999999e24 < k < 1.9000000000000001e64

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   4. Applied rewrites 76.4%

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

   5. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x + a \cdot t\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

      8. lift-*.f64 59.0

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

   7. Applied rewrites 59.0%

      \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \left(a \cdot t\right) + b \cdot \color{blue}{c} \]
   9. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot t + b \cdot c \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot a, t, b \cdot c\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot a, t, b \cdot c\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right) \]

      5. lift-*.f64 42.0

         \[\leadsto \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right) \]

   10. Applied rewrites 42.0%

       \[\leadsto \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right) \]

   if 1.9000000000000001e64 < k < 4.50000000000000009e154

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(a \cdot t\right)} + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(a \cdot t\right)} + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto c \cdot b - \left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      5. distribute-lft-out N/A

         \[\leadsto c \cdot b - \left(4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \color{blue}{a \cdot t + i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, \color{blue}{t}, i \cdot x\right), 27 \cdot \left(j \cdot k\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), 27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i \cdot x}\right), \left(j \cdot k\right) \cdot 27\right) \]

      10. lower-*.f64 N/A

          \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i \cdot x}\right), \left(j \cdot k\right) \cdot 27\right) \]

      11. *-commutative N/A

          \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i} \cdot x\right), \left(k \cdot j\right) \cdot 27\right) \]

      12. lower-*.f64 76.4

          \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i} \cdot x\right), \left(k \cdot j\right) \cdot 27\right) \]

   4. Applied rewrites 76.4%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)} \]

   5. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)} \]
   6. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(\color{blue}{a \cdot t} + i \cdot x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x + a \cdot t\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

      8. lift-*.f64 59.0

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

   7. Applied rewrites 59.0%

      \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

   8. Taylor expanded in b around 0

      \[\leadsto -4 \cdot \left(a \cdot t + \color{blue}{i \cdot x}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t + i \cdot x\right) \cdot -4 \]

      2. +-commutative N/A

         \[\leadsto \left(i \cdot x + a \cdot t\right) \cdot -4 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(i \cdot x + a \cdot t\right) \cdot -4 \]

      4. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]

      5. lift-*.f64 39.6

         \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]

   10. Applied rewrites 39.6%

       \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]

   if 4.50000000000000009e154 < k

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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 24.4

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

   6. Applied rewrites 24.4%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 47.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+220}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -4e+220)
     (* (* -27.0 k) j)
     (if (<= t_1 4e+159) (* (fma i x (* a t)) -4.0) (* (* -27.0 j) k)))))

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 tmp;
	if (t_1 <= -4e+220) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= 4e+159) {
		tmp = fma(i, x, (a * t)) * -4.0;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -4e+220)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (t_1 <= 4e+159)
		tmp = Float64(fma(i, x, Float64(a * t)) * -4.0);
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+220], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, 4e+159], N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4e220

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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 24.4

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

   6. Applied rewrites 24.4%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

   if -4e220 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999997e159

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(a \cdot t\right)} + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto c \cdot b - \left(\color{blue}{4 \cdot \left(a \cdot t\right)} + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto c \cdot b - \left(\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right) + \color{blue}{27 \cdot \left(j \cdot k\right)}\right) \]

      5. distribute-lft-out N/A

         \[\leadsto c \cdot b - \left(4 \cdot \left(a \cdot t + i \cdot x\right) + \color{blue}{27} \cdot \left(j \cdot k\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \color{blue}{a \cdot t + i \cdot x}, 27 \cdot \left(j \cdot k\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, \color{blue}{t}, i \cdot x\right), 27 \cdot \left(j \cdot k\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), 27 \cdot \left(j \cdot k\right)\right) \]

      9. *-commutative N/A

         \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i \cdot x}\right), \left(j \cdot k\right) \cdot 27\right) \]

      10. lower-*.f64 N/A

          \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i \cdot x}\right), \left(j \cdot k\right) \cdot 27\right) \]

      11. *-commutative N/A

          \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i} \cdot x\right), \left(k \cdot j\right) \cdot 27\right) \]

      12. lower-*.f64 76.4

          \[\leadsto c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, \color{blue}{i} \cdot x\right), \left(k \cdot j\right) \cdot 27\right) \]

   4. Applied rewrites 76.4%

      \[\leadsto \color{blue}{c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)} \]

   5. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)} \]
   6. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \color{blue}{\left(a \cdot t + i \cdot x\right)} \]

      2. *-commutative N/A

         \[\leadsto c \cdot b + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(\color{blue}{a \cdot t} + i \cdot x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t + i \cdot x\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x + a \cdot t\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

      8. lift-*.f64 59.0

         \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

   7. Applied rewrites 59.0%

      \[\leadsto \mathsf{fma}\left(c, \color{blue}{b}, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) \]

   8. Taylor expanded in b around 0

      \[\leadsto -4 \cdot \left(a \cdot t + \color{blue}{i \cdot x}\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t + i \cdot x\right) \cdot -4 \]

      2. +-commutative N/A

         \[\leadsto \left(i \cdot x + a \cdot t\right) \cdot -4 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(i \cdot x + a \cdot t\right) \cdot -4 \]

      4. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]

      5. lift-*.f64 39.6

         \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]

   10. Applied rewrites 39.6%

       \[\leadsto \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4 \]

   if 3.9999999999999997e159 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      6. lower-*.f64 24.4

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   6. Applied rewrites 24.4%

      \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 35.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.5 \cdot 10^{-60}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;k \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

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 (<= k -3.5e-60)
   (* (* -27.0 j) k)
   (if (<= k 7.2e+14)
     (* (* a t) -4.0)
     (if (<= k 1.4e+152) (* (* -4.0 i) x) (* (* -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 (k <= -3.5e-60) {
		tmp = (-27.0 * j) * k;
	} else if (k <= 7.2e+14) {
		tmp = (a * t) * -4.0;
	} else if (k <= 1.4e+152) {
		tmp = (-4.0 * i) * x;
	} 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 (k <= (-3.5d-60)) then
        tmp = ((-27.0d0) * j) * k
    else if (k <= 7.2d+14) then
        tmp = (a * t) * (-4.0d0)
    else if (k <= 1.4d+152) then
        tmp = ((-4.0d0) * i) * x
    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 (k <= -3.5e-60) {
		tmp = (-27.0 * j) * k;
	} else if (k <= 7.2e+14) {
		tmp = (a * t) * -4.0;
	} else if (k <= 1.4e+152) {
		tmp = (-4.0 * i) * x;
	} 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 k <= -3.5e-60:
		tmp = (-27.0 * j) * k
	elif k <= 7.2e+14:
		tmp = (a * t) * -4.0
	elif k <= 1.4e+152:
		tmp = (-4.0 * i) * x
	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 (k <= -3.5e-60)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (k <= 7.2e+14)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (k <= 1.4e+152)
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = Float64(Float64(-27.0 * 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 (k <= -3.5e-60)
		tmp = (-27.0 * j) * k;
	elseif (k <= 7.2e+14)
		tmp = (a * t) * -4.0;
	elseif (k <= 1.4e+152)
		tmp = (-4.0 * i) * x;
	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[LessEqual[k, -3.5e-60], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[k, 7.2e+14], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[k, 1.4e+152], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -3.49999999999999976e-60

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      6. lower-*.f64 24.4

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   6. Applied rewrites 24.4%

      \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

   if -3.49999999999999976e-60 < k < 7.2e14

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(-4\right)\right) \cdot a\right) \cdot t \]

      6. metadata-eval N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + 4 \cdot a\right) \cdot t \]

      7. lower-fma.f64 N/A

         \[\leadsto -\mathsf{fma}\left(-18, x \cdot \left(y \cdot z\right), 4 \cdot a\right) \cdot t \]

      8. *-commutative N/A

         \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

      9. lower-*.f64 N/A

         \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

      12. lower-*.f64 42.9

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

   4. Applied rewrites 42.9%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t} \]

   5. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

      3. lift-*.f64 21.4

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

   7. Applied rewrites 21.4%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{-4} \]

   if 7.2e14 < k < 1.4000000000000001e152

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. 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 21.4

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   4. Applied rewrites 21.4%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

   if 1.4000000000000001e152 < k

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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 24.4

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

   6. Applied rewrites 24.4%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 35.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+24}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+24)
     (* (* -27.0 k) j)
     (if (<= t_1 2e+53) (* (* a t) -4.0) (* -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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+24) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= 2e+53) {
		tmp = (a * t) * -4.0;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-1d+24)) then
        tmp = ((-27.0d0) * k) * j
    else if (t_1 <= 2d+53) then
        tmp = (a * t) * (-4.0d0)
    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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+24) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= 2e+53) {
		tmp = (a * t) * -4.0;
	} 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):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+24:
		tmp = (-27.0 * k) * j
	elif t_1 <= 2e+53:
		tmp = (a * t) * -4.0
	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)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -1e+24)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (t_1 <= 2e+53)
		tmp = Float64(Float64(a * t) * -4.0);
	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)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+24)
		tmp = (-27.0 * k) * j;
	elseif (t_1 <= 2e+53)
		tmp = (a * t) * -4.0;
	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_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+24], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, 2e+53], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999998e23

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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 24.4

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

   6. Applied rewrites 24.4%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

   if -9.9999999999999998e23 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e53

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(-4\right)\right) \cdot a\right) \cdot t \]

      6. metadata-eval N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + 4 \cdot a\right) \cdot t \]

      7. lower-fma.f64 N/A

         \[\leadsto -\mathsf{fma}\left(-18, x \cdot \left(y \cdot z\right), 4 \cdot a\right) \cdot t \]

      8. *-commutative N/A

         \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

      9. lower-*.f64 N/A

         \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

      12. lower-*.f64 42.9

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

   4. Applied rewrites 42.9%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t} \]

   5. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

      3. lift-*.f64 21.4

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

   7. Applied rewrites 21.4%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{-4} \]

   if 2e53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 31.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -1e+24) t_1 (if (<= t_2 2e+53) (* (* a t) -4.0) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+24) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-1d+24)) then
        tmp = t_1
    else if (t_2 <= 2d+53) then
        tmp = (a * t) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -1e+24) {
		tmp = t_1;
	} else if (t_2 <= 2e+53) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -1e+24:
		tmp = t_1
	elif t_2 <= 2e+53:
		tmp = (a * t) * -4.0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -1e+24)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		tmp = Float64(Float64(a * t) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -1e+24)
		tmp = t_1;
	elseif (t_2 <= 2e+53)
		tmp = (a * t) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+24], t$95$1, If[LessEqual[t$95$2, 2e+53], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.9999999999999998e23 or 2e53 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 24.4

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -9.9999999999999998e23 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e53

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

      2. lower-neg.f64 N/A

         \[\leadsto -t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

      3. *-commutative N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

      4. lower-*.f64 N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(-4\right)\right) \cdot a\right) \cdot t \]

      6. metadata-eval N/A

         \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + 4 \cdot a\right) \cdot t \]

      7. lower-fma.f64 N/A

         \[\leadsto -\mathsf{fma}\left(-18, x \cdot \left(y \cdot z\right), 4 \cdot a\right) \cdot t \]

      8. *-commutative N/A

         \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

      9. lower-*.f64 N/A

         \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

      10. *-commutative N/A

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

      11. lower-*.f64 N/A

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

      12. lower-*.f64 42.9

          \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

   4. Applied rewrites 42.9%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t} \]

   5. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

      2. lower-*.f64 N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

      3. lift-*.f64 21.4

         \[\leadsto \left(a \cdot t\right) \cdot -4 \]

   7. Applied rewrites 21.4%

      \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{-4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 21.4% accurate, 6.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\\\ [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \left(a \cdot t\right) \cdot -4 \end{array} \]

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 (* (* a t) -4.0))

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) {
	return (a * t) * -4.0;
}

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 = (a * t) * (-4.0d0)
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 (a * t) * -4.0;
}

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 (a * t) * -4.0

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(Float64(a * t) * -4.0)
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 = (a * t) * -4.0;
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[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]

Derivation

1. Initial program 85.4%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

2. Taylor expanded in t around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} \]
3. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right) \]

   2. lower-neg.f64 N/A

      \[\leadsto -t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \]

   3. *-commutative N/A

      \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

   4. lower-*.f64 N/A

      \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right) \cdot t \]

   5. fp-cancel-sub-sign-inv N/A

      \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(-4\right)\right) \cdot a\right) \cdot t \]

   6. metadata-eval N/A

      \[\leadsto -\left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + 4 \cdot a\right) \cdot t \]

   7. lower-fma.f64 N/A

      \[\leadsto -\mathsf{fma}\left(-18, x \cdot \left(y \cdot z\right), 4 \cdot a\right) \cdot t \]

   8. *-commutative N/A

      \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

   9. lower-*.f64 N/A

      \[\leadsto -\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot x, 4 \cdot a\right) \cdot t \]

   10. *-commutative N/A

       \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

   11. lower-*.f64 N/A

       \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

   12. lower-*.f64 42.9

       \[\leadsto -\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t \]

4. Applied rewrites 42.9%

   \[\leadsto \color{blue}{-\mathsf{fma}\left(-18, \left(z \cdot y\right) \cdot x, 4 \cdot a\right) \cdot t} \]

5. Taylor expanded in x around 0

   \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(a \cdot t\right) \cdot -4 \]

   2. lower-*.f64 N/A

      \[\leadsto \left(a \cdot t\right) \cdot -4 \]

   3. lift-*.f64 21.4

      \[\leadsto \left(a \cdot t\right) \cdot -4 \]

7. Applied rewrites 21.4%

   \[\leadsto \left(a \cdot t\right) \cdot \color{blue}{-4} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025136 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))