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

Percentage Accurate: 85.6% → 92.4%

Time: 7.1s

Alternatives: 20

Speedup: 0.5×

• 50.0% 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: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ t_2 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ t_3 := t\_2 - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_2 - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right), x, c \cdot b\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* k j) 27.0 (* (* a t) 4.0)))
        (t_2
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i)))
        (t_3 (- t_2 (* (* j 27.0) k))))
   (if (<= t_3 -1e+178)
     (- (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b)) t_1)
     (if (<= t_3 2e+296)
       (- t_2 (* j (* k 27.0)))
       (if (<= t_3 INFINITY)
         (- (fma (fma (* (* t z) 18.0) y (* -4.0 i)) x (* c b)) t_1)
         (fma
          (* -4.0 a)
          t
          (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);
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, ((a * t) * 4.0));
	double t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double t_3 = t_2 - ((j * 27.0) * k);
	double tmp;
	if (t_3 <= -1e+178) {
		tmp = fma(fma((18.0 * t), (z * y), (-4.0 * i)), x, (c * b)) - t_1;
	} else if (t_3 <= 2e+296) {
		tmp = t_2 - (j * (k * 27.0));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = fma(fma(((t * z) * 18.0), y, (-4.0 * i)), x, (c * b)) - t_1;
	} else {
		tmp = fma((-4.0 * a), t, 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * j), 27.0, Float64(Float64(a * t) * 4.0))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	t_3 = Float64(t_2 - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_3 <= -1e+178)
		tmp = Float64(fma(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)), x, Float64(c * b)) - t_1);
	elseif (t_3 <= 2e+296)
		tmp = Float64(t_2 - Float64(j * Float64(k * 27.0)));
	elseif (t_3 <= Inf)
		tmp = Float64(fma(fma(Float64(Float64(t * z) * 18.0), y, Float64(-4.0 * i)), x, Float64(c * b)) - t_1);
	else
		tmp = fma(Float64(-4.0 * a), t, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * 27.0 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(t$95$2 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+178], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e+296], N[(t$95$2 - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t + 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 4 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < -1.0000000000000001e178

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.6%

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

   if -1.0000000000000001e178 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < 1.99999999999999996e296

   1. Initial program 99.8%

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

      1. lift-*.f64 N/A

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

      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 99.9

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

   4. Applied rewrites 99.9%

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

   if 1.99999999999999996e296 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 90.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 93.3

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

   7. Applied rewrites 93.3%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 29.4%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 70.6%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 4\right) \cdot i\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - t\_1\right) - t\_2\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\left(18 \cdot x\right) \cdot y, z \cdot t, \left(\left(-4\right) \cdot a\right) \cdot t\right) + b \cdot c\right) - t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i))
        (t_2 (* (* j 27.0) k))
        (t_3
         (-
          (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) t_1)
          t_2)))
   (if (<= t_3 -1e+178)
     (-
      (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b))
      (fma (* k j) 27.0 (* (* a t) 4.0)))
     (if (<= t_3 INFINITY)
       (-
        (- (+ (fma (* (* 18.0 x) y) (* z t) (* (* (- 4.0) a) t)) (* b c)) t_1)
        t_2)
       (fma
        (* -4.0 a)
        t
        (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);
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 * 4.0) * i;
	double t_2 = (j * 27.0) * k;
	double t_3 = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - t_1) - t_2;
	double tmp;
	if (t_3 <= -1e+178) {
		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 (t_3 <= ((double) INFINITY)) {
		tmp = ((fma(((18.0 * x) * y), (z * t), ((-4.0 * a) * t)) + (b * c)) - t_1) - t_2;
	} else {
		tmp = fma((-4.0 * a), t, 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 4.0) * i)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - t_1) - t_2)
	tmp = 0.0
	if (t_3 <= -1e+178)
		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 (t_3 <= Inf)
		tmp = Float64(Float64(Float64(fma(Float64(Float64(18.0 * x) * y), Float64(z * t), Float64(Float64(Float64(-4.0) * a) * t)) + Float64(b * c)) - t_1) - t_2);
	else
		tmp = fma(Float64(-4.0 * a), t, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+178], 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[t$95$3, Infinity], N[(N[(N[(N[(N[(N[(18.0 * x), $MachinePrecision] * y), $MachinePrecision] * N[(z * t), $MachinePrecision] + N[(N[((-4.0) * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t + 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 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < -1.0000000000000001e178

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.6%

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

   if -1.0000000000000001e178 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 94.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 95.4

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

   4. Applied rewrites 95.4%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 29.4%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 70.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\left(18 \cdot x\right) \cdot y, z \cdot t, \left(\left(-4\right) \cdot a\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ t_2 := \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right), x, c \cdot b\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* k j) 27.0 (* (* a t) 4.0)))
        (t_2
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_2 -5e+183)
     (- (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b)) t_1)
     (if (<= t_2 INFINITY)
       (- (fma (fma (* (* t z) 18.0) y (* -4.0 i)) x (* c b)) t_1)
       (fma
        (* -4.0 a)
        t
        (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);
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, ((a * t) * 4.0));
	double t_2 = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	double tmp;
	if (t_2 <= -5e+183) {
		tmp = fma(fma((18.0 * t), (z * y), (-4.0 * i)), x, (c * b)) - t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma(fma(((t * z) * 18.0), y, (-4.0 * i)), x, (c * b)) - t_1;
	} else {
		tmp = fma((-4.0 * a), t, 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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * j), 27.0, Float64(Float64(a * t) * 4.0))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_2 <= -5e+183)
		tmp = Float64(fma(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)), x, Float64(c * b)) - t_1);
	elseif (t_2 <= Inf)
		tmp = Float64(fma(fma(Float64(Float64(t * z) * 18.0), y, Float64(-4.0 * i)), x, Float64(c * b)) - t_1);
	else
		tmp = fma(Float64(-4.0 * a), t, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * 27.0 + N[(N[(a * t), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+183], N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t + 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 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < -5.00000000000000009e183

   1. Initial program 91.1%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 98.6%

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

   if -5.00000000000000009e183 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 91.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 94.0

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

   7. Applied rewrites 94.0%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 29.4%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 70.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+183}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right), x, c \cdot b\right) - \mathsf{fma}\left(k \cdot j, 27, \left(a \cdot t\right) \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+260} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+299}\right):\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \left(k \cdot 27\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 (or (<= t_1 -5e+260) (not (<= t_1 5e+299)))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
     (- (* c b) (* (* k 27.0) j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if ((t_1 <= -5e+260) || !(t_1 <= 5e+299)) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else {
		tmp = (c * b) - ((k * 27.0) * 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])
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 <= -5e+260) || !(t_1 <= 5e+299))
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	else
		tmp = Float64(Float64(c * b) - Float64(Float64(k * 27.0) * 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.
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[Or[LessEqual[t$95$1, -5e+260], N[Not[LessEqual[t$95$1, 5e+299]], $MachinePrecision]], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(N[(k * 27.0), $MachinePrecision] * j), $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)) < -4.9999999999999996e260 or 5.0000000000000003e299 < (-.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 63.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 65.3

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

   5. Applied rewrites 65.3%

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

   if -4.9999999999999996e260 < (-.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)) < 5.0000000000000003e299

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 59.4

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

   7. Applied rewrites 59.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -5 \cdot 10^{+260} \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+299}\right):\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \left(k \cdot 27\right) \cdot j\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+260}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;c \cdot b - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 -5e+260)
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
     (if (<= t_1 5e+299)
       (- (* c b) (* (* k 27.0) j))
       (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -5e+260) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else if (t_1 <= 5e+299) {
		tmp = (c * b) - ((k * 27.0) * j);
	} else {
		tmp = fma(((z * y) * x), 18.0, (-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])
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 <= -5e+260)
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	elseif (t_1 <= 5e+299)
		tmp = Float64(Float64(c * b) - Float64(Float64(k * 27.0) * j));
	else
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, 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.
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, -5e+260], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+299], N[(N[(c * b), $MachinePrecision] - N[(N[(k * 27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $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)) < -4.9999999999999996e260

   1. Initial program 80.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -4.9999999999999996e260 < (-.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)) < 5.0000000000000003e299

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 59.4

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

   7. Applied rewrites 59.4%

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

   if 5.0000000000000003e299 < (-.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 51.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 58.4

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

   5. Applied rewrites 58.4%

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

Alternative 6: 55.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+260}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;c \cdot b - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, 18 \cdot x, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 -5e+260)
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
     (if (<= t_1 5e+299)
       (- (* c b) (* (* k 27.0) j))
       (* (fma (* z y) (* 18.0 x) (* -4.0 a)) t)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -5e+260) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else if (t_1 <= 5e+299) {
		tmp = (c * b) - ((k * 27.0) * j);
	} else {
		tmp = fma((z * y), (18.0 * x), (-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])
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 <= -5e+260)
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	elseif (t_1 <= 5e+299)
		tmp = Float64(Float64(c * b) - Float64(Float64(k * 27.0) * j));
	else
		tmp = Float64(fma(Float64(z * y), Float64(18.0 * x), 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.
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, -5e+260], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+299], N[(N[(c * b), $MachinePrecision] - N[(N[(k * 27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * y), $MachinePrecision] * N[(18.0 * x), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $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)) < -4.9999999999999996e260

   1. Initial program 80.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -4.9999999999999996e260 < (-.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)) < 5.0000000000000003e299

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 59.4

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

   7. Applied rewrites 59.4%

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

   if 5.0000000000000003e299 < (-.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 51.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 58.4

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

   5. Applied rewrites 58.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 58.4

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

   7. Applied rewrites 58.4%

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

Alternative 7: 90.5% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<=
      (-
       (-
        (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
        (* (* x 4.0) i))
       (* (* j 27.0) k))
      INFINITY)
   (-
    (fma (fma (* 18.0 t) (* z y) (* -4.0 i)) x (* c b))
    (fma (* k j) 27.0 (* (* a t) 4.0)))
   (fma (* -4.0 a) t (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);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = fma(fma((18.0 * t), (z * y), (-4.0 * i)), x, (c * b)) - fma((k * j), 27.0, ((a * t) * 4.0));
	} else {
		tmp = fma((-4.0 * a), t, 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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = Float64(fma(fma(Float64(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)));
	else
		tmp = fma(Float64(-4.0 * a), t, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(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], N[(N[(-4.0 * a), $MachinePrecision] * t + 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 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 93.9%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 29.4%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 70.6%

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

4. Final simplification 90.8%

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

Alternative 8: 35.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot i\right) \cdot x\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+110}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-273}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_2 \leq 5000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+99}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* -4.0 i) x)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+110)
     (* -27.0 (* k j))
     (if (<= t_2 -1e-180)
       t_1
       (if (<= t_2 4e-273)
         (* c b)
         (if (<= t_2 5000000000.0)
           t_1
           (if (<= t_2 2e+99) (* -4.0 (* a t)) (* (* -27.0 k) j))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * i) * x;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+110) {
		tmp = -27.0 * (k * j);
	} else if (t_2 <= -1e-180) {
		tmp = t_1;
	} else if (t_2 <= 4e-273) {
		tmp = c * b;
	} else if (t_2 <= 5000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+99) {
		tmp = -4.0 * (a * t);
	} 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.
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 = ((-4.0d0) * i) * x
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+110)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_2 <= (-1d-180)) then
        tmp = t_1
    else if (t_2 <= 4d-273) then
        tmp = c * b
    else if (t_2 <= 5000000000.0d0) then
        tmp = t_1
    else if (t_2 <= 2d+99) then
        tmp = (-4.0d0) * (a * t)
    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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (-4.0 * i) * x;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+110) {
		tmp = -27.0 * (k * j);
	} else if (t_2 <= -1e-180) {
		tmp = t_1;
	} else if (t_2 <= 4e-273) {
		tmp = c * b;
	} else if (t_2 <= 5000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+99) {
		tmp = -4.0 * (a * t);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * i) * x
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+110:
		tmp = -27.0 * (k * j)
	elif t_2 <= -1e-180:
		tmp = t_1
	elif t_2 <= 4e-273:
		tmp = c * b
	elif t_2 <= 5000000000.0:
		tmp = t_1
	elif t_2 <= 2e+99:
		tmp = -4.0 * (a * t)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * i) * x)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+110)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_2 <= -1e-180)
		tmp = t_1;
	elseif (t_2 <= 4e-273)
		tmp = Float64(c * b);
	elseif (t_2 <= 5000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2e+99)
		tmp = Float64(-4.0 * Float64(a * t));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (-4.0 * i) * x;
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+110)
		tmp = -27.0 * (k * j);
	elseif (t_2 <= -1e-180)
		tmp = t_1;
	elseif (t_2 <= 4e-273)
		tmp = c * b;
	elseif (t_2 <= 5000000000.0)
		tmp = t_1;
	elseif (t_2 <= 2e+99)
		tmp = -4.0 * (a * t);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+110], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-180], t$95$1, If[LessEqual[t$95$2, 4e-273], N[(c * b), $MachinePrecision], If[LessEqual[t$95$2, 5000000000.0], t$95$1, If[LessEqual[t$95$2, 2e+99], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e110

   1. Initial program 76.6%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 55.5

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

   5. Applied rewrites 55.5%

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

   if -2e110 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1e-180 or 4e-273 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5e9

   1. Initial program 82.1%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 32.7

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

   5. Applied rewrites 32.7%

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

   if -1e-180 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4e-273

   1. Initial program 87.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 41.6

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

   5. Applied rewrites 41.6%

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

   if 5e9 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e99

   1. Initial program 82.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.3

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

   5. Applied rewrites 41.3%

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

   if 1.9999999999999999e99 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 76.0%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.0

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

   5. Applied rewrites 68.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 68.0

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

   7. Applied rewrites 68.0%

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

Alternative 9: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+90} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+107}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right), x, c \cdot b\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -1e+90) (not (<= t_1 5e+107)))
     (- (fma (fma (* (* t z) 18.0) y (* -4.0 i)) x (* c b)) (* (* k j) 27.0))
     (fma (* -4.0 a) t (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);
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+90) || !(t_1 <= 5e+107)) {
		tmp = fma(fma(((t * z) * 18.0), y, (-4.0 * i)), x, (c * b)) - ((k * j) * 27.0);
	} else {
		tmp = fma((-4.0 * a), t, 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])
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+90) || !(t_1 <= 5e+107))
		tmp = Float64(fma(fma(Float64(Float64(t * z) * 18.0), y, Float64(-4.0 * i)), x, Float64(c * b)) - Float64(Float64(k * j) * 27.0));
	else
		tmp = fma(Float64(-4.0 * a), t, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+90], N[Not[LessEqual[t$95$1, 5e+107]], $MachinePrecision]], N[(N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t + 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 j #s(literal 27 binary64)) k) < -9.99999999999999966e89 or 5.0000000000000002e107 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 77.1%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 81.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 81.6

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

   7. Applied rewrites 81.6%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 81.6

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

   10. Applied rewrites 81.6%

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

   if -9.99999999999999966e89 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e107

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 88.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+90} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+107}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right), x, c \cdot b\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+90} \lor \neg \left(t\_2 \leq 5 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (fma (* (* z y) t) 18.0 (* -4.0 i)) x (* c b)))
        (t_2 (* (* j 27.0) k)))
   (if (or (<= t_2 -1e+90) (not (<= t_2 5e+96)))
     (fma (* k j) -27.0 t_1)
     (fma (* -4.0 a) t t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(fma(((z * y) * t), 18.0, (-4.0 * i)), x, (c * b));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -1e+90) || !(t_2 <= 5e+96)) {
		tmp = fma((k * j), -27.0, t_1);
	} else {
		tmp = fma((-4.0 * a), t, t_1);
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)), x, Float64(c * b))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_2 <= -1e+90) || !(t_2 <= 5e+96))
		tmp = fma(Float64(k * j), -27.0, t_1);
	else
		tmp = fma(Float64(-4.0 * a), t, t_1);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -1e+90], N[Not[LessEqual[t$95$2, 5e+96]], $MachinePrecision]], N[(N[(k * j), $MachinePrecision] * -27.0 + t$95$1), $MachinePrecision], N[(N[(-4.0 * a), $MachinePrecision] * t + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -9.99999999999999966e89 or 5.0000000000000004e96 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 81.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 81.0

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

   7. Applied rewrites 81.0%

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

   8. Taylor expanded in a around 0

      \[\leadsto \left(b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right) - \color{blue}{27 \cdot \left(j \cdot k\right)} \]
   9. 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

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

   10. Applied rewrites 81.5%

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

   if -9.99999999999999966e89 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000004e96

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 88.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -1 \cdot 10^{+90} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+96}\right):\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot t\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \left(k \cdot j\right) \cdot 27\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(t\_1 \cdot 18, x, c \cdot b\right) - t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(t\_1, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4 - t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) t)) (t_2 (* (* j 27.0) k)) (t_3 (* (* k j) 27.0)))
   (if (<= t_2 -5e+118)
     (- (fma (* t_1 18.0) x (* c b)) t_3)
     (if (<= t_2 2e+99)
       (fma (* -4.0 a) t (fma (fma t_1 18.0 (* -4.0 i)) x (* c b)))
       (- (* (* i x) -4.0) t_3)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * t;
	double t_2 = (j * 27.0) * k;
	double t_3 = (k * j) * 27.0;
	double tmp;
	if (t_2 <= -5e+118) {
		tmp = fma((t_1 * 18.0), x, (c * b)) - t_3;
	} else if (t_2 <= 2e+99) {
		tmp = fma((-4.0 * a), t, fma(fma(t_1, 18.0, (-4.0 * i)), x, (c * b)));
	} else {
		tmp = ((i * x) * -4.0) - t_3;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * t)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(Float64(k * j) * 27.0)
	tmp = 0.0
	if (t_2 <= -5e+118)
		tmp = Float64(fma(Float64(t_1 * 18.0), x, Float64(c * b)) - t_3);
	elseif (t_2 <= 2e+99)
		tmp = fma(Float64(-4.0 * a), t, fma(fma(t_1, 18.0, Float64(-4.0 * i)), x, Float64(c * b)));
	else
		tmp = Float64(Float64(Float64(i * x) * -4.0) - t_3);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+118], N[(N[(N[(t$95$1 * 18.0), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 2e+99], N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(t$95$1 * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999972e118

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 78.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 78.8

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

   7. Applied rewrites 78.8%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 81.2

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

   10. Applied rewrites 81.2%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 72.5

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

   13. Applied rewrites 72.5%

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

   if -4.99999999999999972e118 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e99

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. +-commutative N/A

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

   8. Applied rewrites 88.3%

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

   if 1.9999999999999999e99 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 82.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 80.5

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

   7. Applied rewrites 80.5%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 78.5

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

   10. Applied rewrites 78.5%

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

   11. Taylor expanded in i around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift-*.f64 78.5

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

   13. Applied rewrites 78.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+118}:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot t\right) \cdot 18, x, c \cdot b\right) - \left(k \cdot j\right) \cdot 27\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right), x, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4 - \left(k \cdot j\right) \cdot 27\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+173}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-52}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+99}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+173)
     (* -27.0 (* k j))
     (if (<= t_1 4e-52)
       (* c b)
       (if (<= t_1 2e+99) (* -4.0 (* a t)) (* (* -27.0 k) j))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+173) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 4e-52) {
		tmp = c * b;
	} else if (t_1 <= 2e+99) {
		tmp = -4.0 * (a * t);
	} 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+173)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= 4d-52) then
        tmp = c * b
    else if (t_1 <= 2d+99) then
        tmp = (-4.0d0) * (a * t)
    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;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+173) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 4e-52) {
		tmp = c * b;
	} else if (t_1 <= 2e+99) {
		tmp = -4.0 * (a * t);
	} 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])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+173:
		tmp = -27.0 * (k * j)
	elif t_1 <= 4e-52:
		tmp = c * b
	elif t_1 <= 2e+99:
		tmp = -4.0 * (a * t)
	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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+173)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 4e-52)
		tmp = Float64(c * b);
	elseif (t_1 <= 2e+99)
		tmp = Float64(-4.0 * Float64(a * t));
	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])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+173)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 4e-52)
		tmp = c * b;
	elseif (t_1 <= 2e+99)
		tmp = -4.0 * (a * t);
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+173], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e-52], N[(c * b), $MachinePrecision], If[LessEqual[t$95$1, 2e+99], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e173

   1. Initial program 68.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -2e173 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4e-52

   1. Initial program 84.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 29.8

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

   5. Applied rewrites 29.8%

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

   if 4e-52 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e99

   1. Initial program 84.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   5. Applied rewrites 34.6%

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

   if 1.9999999999999999e99 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 76.0%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.0

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

   5. Applied rewrites 68.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 68.0

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

   7. Applied rewrites 68.0%

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

Alternative 13: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-52}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+99}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+173)
     t_1
     (if (<= t_2 4e-52) (* c b) (if (<= t_2 2e+99) (* -4.0 (* a t)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+173) {
		tmp = t_1;
	} else if (t_2 <= 4e-52) {
		tmp = c * b;
	} else if (t_2 <= 2e+99) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+173)) then
        tmp = t_1
    else if (t_2 <= 4d-52) then
        tmp = c * b
    else if (t_2 <= 2d+99) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+173) {
		tmp = t_1;
	} else if (t_2 <= 4e-52) {
		tmp = c * b;
	} else if (t_2 <= 2e+99) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+173:
		tmp = t_1
	elif t_2 <= 4e-52:
		tmp = c * b
	elif t_2 <= 2e+99:
		tmp = -4.0 * (a * t)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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 <= -2e+173)
		tmp = t_1;
	elseif (t_2 <= 4e-52)
		tmp = Float64(c * b);
	elseif (t_2 <= 2e+99)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+173)
		tmp = t_1;
	elseif (t_2 <= 4e-52)
		tmp = c * b;
	elseif (t_2 <= 2e+99)
		tmp = -4.0 * (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+173], t$95$1, If[LessEqual[t$95$2, 4e-52], N[(c * b), $MachinePrecision], If[LessEqual[t$95$2, 2e+99], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e173 or 1.9999999999999999e99 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 73.2%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.2

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

   5. Applied rewrites 68.2%

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

   if -2e173 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4e-52

   1. Initial program 84.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 29.8

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

   5. Applied rewrites 29.8%

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

   if 4e-52 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999999e99

   1. Initial program 84.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 34.6

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

   5. Applied rewrites 34.6%

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

Alternative 14: 53.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+38}:\\ \;\;\;\;c \cdot b - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq -4:\\ \;\;\;\;\left(\left(\left(y \cdot x\right) \cdot 18\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;b \cdot c \leq 10^{-7}:\\ \;\;\;\;\left(i \cdot x\right) \cdot -4 - \left(k \cdot j\right) \cdot 27\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+38)
   (- (* c b) (* (* j 27.0) k))
   (if (<= (* b c) -4.0)
     (* (* (* (* y x) 18.0) z) t)
     (if (<= (* b c) 1e-7)
       (- (* (* i x) -4.0) (* (* k j) 27.0))
       (fma (* i x) -4.0 (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+38) {
		tmp = (c * b) - ((j * 27.0) * k);
	} else if ((b * c) <= -4.0) {
		tmp = (((y * x) * 18.0) * z) * t;
	} else if ((b * c) <= 1e-7) {
		tmp = ((i * x) * -4.0) - ((k * j) * 27.0);
	} else {
		tmp = fma((i * x), -4.0, (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+38)
		tmp = Float64(Float64(c * b) - Float64(Float64(j * 27.0) * k));
	elseif (Float64(b * c) <= -4.0)
		tmp = Float64(Float64(Float64(Float64(y * x) * 18.0) * z) * t);
	elseif (Float64(b * c) <= 1e-7)
		tmp = Float64(Float64(Float64(i * x) * -4.0) - Float64(Float64(k * j) * 27.0));
	else
		tmp = fma(Float64(i * x), -4.0, Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+38], N[(N[(c * b), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4.0], N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-7], N[(N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision] - N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.9999999999999997e38

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 65.9

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

   5. Applied rewrites 65.9%

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

   if -4.9999999999999997e38 < (*.f64 b c) < -4

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 70.9

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

   8. Applied rewrites 70.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 N/A

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

      16. lift-*.f64 79.9

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

   10. Applied rewrites 79.9%

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

   if -4 < (*.f64 b c) < 9.9999999999999995e-8

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 88.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 86.5

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

   7. Applied rewrites 86.5%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 72.5

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

   10. Applied rewrites 72.5%

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

   11. Taylor expanded in i around inf

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

       1. *-commutative N/A

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

       2. lift-*.f64 N/A

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

       3. lift-*.f64 53.2

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

   13. Applied rewrites 53.2%

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

   if 9.9999999999999995e-8 < (*.f64 b c)

   1. Initial program 74.9%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 69.8

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 67.1

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

   8. Applied rewrites 67.1%

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

Alternative 15: 71.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(k \cdot j\right) \cdot 27\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, 18 \cdot x, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot t\right) \cdot 18, x, c \cdot b\right) - t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+90}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* k j) 27.0)))
   (if (<= t -1.15e+191)
     (* (fma (* z y) (* 18.0 x) (* -4.0 a)) t)
     (if (<= t -2.25e-69)
       (- (fma (* (* (* z y) t) 18.0) x (* c b)) t_1)
       (if (<= t 2.9e+90)
         (- (* c b) (fma (* i x) 4.0 t_1))
         (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * j) * 27.0;
	double tmp;
	if (t <= -1.15e+191) {
		tmp = fma((z * y), (18.0 * x), (-4.0 * a)) * t;
	} else if (t <= -2.25e-69) {
		tmp = fma((((z * y) * t) * 18.0), x, (c * b)) - t_1;
	} else if (t <= 2.9e+90) {
		tmp = (c * b) - fma((i * x), 4.0, t_1);
	} else {
		tmp = fma(((z * y) * x), 18.0, (-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])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(k * j) * 27.0)
	tmp = 0.0
	if (t <= -1.15e+191)
		tmp = Float64(fma(Float64(z * y), Float64(18.0 * x), Float64(-4.0 * a)) * t);
	elseif (t <= -2.25e-69)
		tmp = Float64(fma(Float64(Float64(Float64(z * y) * t) * 18.0), x, Float64(c * b)) - t_1);
	elseif (t <= 2.9e+90)
		tmp = Float64(Float64(c * b) - fma(Float64(i * x), 4.0, t_1));
	else
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]}, If[LessEqual[t, -1.15e+191], N[(N[(N[(z * y), $MachinePrecision] * N[(18.0 * x), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -2.25e-69], N[(N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision] * x + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.9e+90], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e191

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*l* N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lift-*.f64 76.4

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

   7. Applied rewrites 76.4%

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

   if -1.15e191 < t < -2.25000000000000005e-69

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 83.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 83.0

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

   7. Applied rewrites 83.0%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 87.3

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

   10. Applied rewrites 87.3%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 75.0

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

   13. Applied rewrites 75.0%

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

   if -2.25000000000000005e-69 < t < 2.9000000000000001e90

   1. Initial program 83.8%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if 2.9000000000000001e90 < t

   1. Initial program 79.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 72.1

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

   5. Applied rewrites 72.1%

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

Alternative 16: 52.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+110}:\\ \;\;\;\;c \cdot b - t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+110)
     (- (* c b) t_1)
     (if (<= t_1 5e+111) (fma (* i x) -4.0 (* c b)) (* (* -27.0 k) j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+110) {
		tmp = (c * b) - t_1;
	} else if (t_1 <= 5e+111) {
		tmp = fma((i * x), -4.0, (c * b));
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+110)
		tmp = Float64(Float64(c * b) - t_1);
	elseif (t_1 <= 5e+111)
		tmp = fma(Float64(i * x), -4.0, Float64(c * b));
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+110], N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e+111], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e110

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 66.6

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

   5. Applied rewrites 66.6%

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

   if -2e110 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e111

   1. Initial program 83.8%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 54.0

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

   5. Applied rewrites 54.0%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 51.2

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

   8. Applied rewrites 51.2%

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

   if 4.9999999999999997e111 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 70.9

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

   7. Applied rewrites 70.9%

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

Alternative 17: 51.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+173}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot x, -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+173)
     (* -27.0 (* k j))
     (if (<= t_1 5e+111) (fma (* i x) -4.0 (* c b)) (* (* -27.0 k) j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+173) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+111) {
		tmp = fma((i * x), -4.0, (c * b));
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+173)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 5e+111)
		tmp = fma(Float64(i * x), -4.0, Float64(c * b));
	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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+173], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+111], N[(N[(i * x), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e173

   1. Initial program 68.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -2e173 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999997e111

   1. Initial program 84.5%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 55.8

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

   5. Applied rewrites 55.8%

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

   6. Taylor expanded in j around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 51.2

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

   8. Applied rewrites 51.2%

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

   if 4.9999999999999997e111 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 70.9

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

   5. Applied rewrites 70.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 70.9

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

   7. Applied rewrites 70.9%

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

Alternative 18: 36.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+173} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+85}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -2e+173) (not (<= t_1 5e+85))) (* -27.0 (* k j)) (* c b))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+173) || !(t_1 <= 5e+85)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-2d+173)) .or. (.not. (t_1 <= 5d+85))) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -2e+173) || !(t_1 <= 5e+85)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -2e+173) or not (t_1 <= 5e+85):
		tmp = -27.0 * (k * j)
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -2e+173) || !(t_1 <= 5e+85))
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -2e+173) || ~((t_1 <= 5e+85)))
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+173], N[Not[LessEqual[t$95$1, 5e+85]], $MachinePrecision]], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e173 or 5.0000000000000001e85 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 72.1%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 64.9

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

   5. Applied rewrites 64.9%

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

   if -2e173 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000001e85

   1. Initial program 85.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 28.6

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

   5. Applied rewrites 28.6%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+173} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+85}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, z, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+90}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -3e+37)
   (* (fma (* (* y x) 18.0) z (* -4.0 a)) t)
   (if (<= t 2.9e+90)
     (- (* c b) (fma (* i x) 4.0 (* (* k j) 27.0)))
     (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -3e+37) {
		tmp = fma(((y * x) * 18.0), z, (-4.0 * a)) * t;
	} else if (t <= 2.9e+90) {
		tmp = (c * b) - fma((i * x), 4.0, ((k * j) * 27.0));
	} else {
		tmp = fma(((z * y) * x), 18.0, (-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])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -3e+37)
		tmp = Float64(fma(Float64(Float64(y * x) * 18.0), z, Float64(-4.0 * a)) * t);
	elseif (t <= 2.9e+90)
		tmp = Float64(Float64(c * b) - fma(Float64(i * x), 4.0, Float64(Float64(k * j) * 27.0)));
	else
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, 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.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -3e+37], N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * z + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.9e+90], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.00000000000000022e37

   1. Initial program 77.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 69.1

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

   5. Applied rewrites 69.1%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. associate-*r* N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. *-commutative N/A

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

      19. lower-*.f64 N/A

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

      20. lift-*.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if -3.00000000000000022e37 < t < 2.9000000000000001e90

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 73.2

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

   5. Applied rewrites 73.2%

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

   if 2.9000000000000001e90 < t

   1. Initial program 79.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right) \cdot t \]

      4. *-commutative N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18 + \left(\mathsf{neg}\left(4\right)\right) \cdot a\right) \cdot t \]

      5. metadata-eval N/A

         \[\leadsto \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18 + -4 \cdot a\right) \cdot t \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x \cdot \left(y \cdot z\right), 18, -4 \cdot a\right) \cdot t \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      8. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      9. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

      11. lower-*.f64 72.1

          \[\leadsto \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t \]

   5. Applied rewrites 72.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 24.7% accurate, 11.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = c * b
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return c * b;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(c * b)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = c * b;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 81.1%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Add Preprocessing

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto c \cdot \color{blue}{b} \]

   2. lower-*.f64 21.9

      \[\leadsto c \cdot \color{blue}{b} \]

5. Applied rewrites 21.9%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025057 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))