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

Percentage Accurate: 85.1% → 91.5%

Time: 6.0s

Alternatives: 25

Speedup: 1.0×

• 49.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.5% accurate, 0.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 (* (* j 27.0) k)) INFINITY)
     (- t_1 (* j (* k 27.0)))
     (* (* (fma (* t y) 18.0 (* (/ i z) -4.0)) z) x))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 95.4

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

   3. Applied rewrites 95.4%

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

   if +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. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 58.2

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

   4. Applied rewrites 58.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 58.7

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

   7. Applied rewrites 58.7%

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

Alternative 2: 91.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.4%

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

   2. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 94.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 95.5

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

   6. Applied rewrites 95.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 58.2

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

   4. Applied rewrites 58.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 58.7

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

   7. Applied rewrites 58.7%

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

Alternative 3: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(y \cdot \left(z \cdot x\right)\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\right)\\ \end{array} \end{array} \]

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 2e-6)
   (-
    (fma
     (* -4.0 i)
     x
     (fma (* -4.0 a) t (fma (* (* y (* z x)) t) 18.0 (* c b))))
    (* (* j 27.0) k))
   (fma
    (* -27.0 j)
    k
    (fma (* 18.0 t) (* (* z y) x) (- (* c b) (* 4.0 (fma a t (* i x))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= 2e-6) {
		tmp = fma((-4.0 * i), x, fma((-4.0 * a), t, fma(((y * (z * x)) * t), 18.0, (c * b)))) - ((j * 27.0) * k);
	} else {
		tmp = fma((-27.0 * j), k, fma((18.0 * t), ((z * y) * x), ((c * b) - (4.0 * fma(a, t, (i * x))))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 2e-6)
		tmp = Float64(fma(Float64(-4.0 * i), x, fma(Float64(-4.0 * a), t, fma(Float64(Float64(y * Float64(z * x)) * t), 18.0, Float64(c * b)))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(18.0 * t), Float64(Float64(z * y) * x), Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x))))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 2e-6], N[(N[(N[(-4.0 * i), $MachinePrecision] * x + N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(18.0 * t), $MachinePrecision] * N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.99999999999999991e-6

   1. Initial program 88.3%

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

   2. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 89.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 91.1

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

   6. Applied rewrites 91.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 91.2

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

   8. Applied rewrites 91.2%

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

   if 1.99999999999999991e-6 < x

   1. Initial program 75.4%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 82.8%

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

Alternative 4: 89.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.6%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 93.1%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 67.2

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

   4. Applied rewrites 67.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 67.1

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

   7. Applied rewrites 67.1%

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

Alternative 5: 72.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, \left(-4 \cdot a\right) \cdot t\right) - t\_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -9.8e+86)
     (* (fma (* (* t z) 18.0) y (* -4.0 i)) x)
     (if (<= x -4.5e+23)
       (- (fma (* -4.0 i) x (* (* -4.0 a) t)) t_1)
       (if (<= x 2.6e+140)
         (- (fma c b (* -4.0 (* a t))) t_1)
         (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 (x <= -9.8e+86) {
		tmp = fma(((t * z) * 18.0), y, (-4.0 * i)) * x;
	} else if (x <= -4.5e+23) {
		tmp = fma((-4.0 * i), x, ((-4.0 * a) * t)) - t_1;
	} else if (x <= 2.6e+140) {
		tmp = fma(c, b, (-4.0 * (a * t))) - t_1;
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -9.8e+86)
		tmp = Float64(fma(Float64(Float64(t * z) * 18.0), y, Float64(-4.0 * i)) * x);
	elseif (x <= -4.5e+23)
		tmp = Float64(fma(Float64(-4.0 * i), x, Float64(Float64(-4.0 * a) * t)) - t_1);
	elseif (x <= 2.6e+140)
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - t_1);
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
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[x, -9.8e+86], N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -4.5e+23], N[(N[(N[(-4.0 * i), $MachinePrecision] * x + N[(N[(-4.0 * a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 2.6e+140], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.7999999999999999e86

   1. Initial program 72.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 68.7

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

   4. Applied rewrites 68.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 69.4

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

   6. Applied rewrites 69.4%

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

   if -9.7999999999999999e86 < x < -4.49999999999999979e23

   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. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 90.2%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 60.6

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

   7. Applied rewrites 60.6%

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

   if -4.49999999999999979e23 < x < 2.6000000000000001e140

   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. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 73.6

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

   4. Applied rewrites 73.6%

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

   if 2.6000000000000001e140 < x

   1. Initial program 71.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 71.9

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

   4. Applied rewrites 71.9%

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

Alternative 6: 71.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -8e+23)
   (* (fma (* (* t z) 18.0) y (* -4.0 i)) x)
   (if (<= x 2.6e+140)
     (- (fma c b (* -4.0 (* a t))) (* (* j 27.0) k))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -8e+23) {
		tmp = fma(((t * z) * 18.0), y, (-4.0 * i)) * x;
	} else if (x <= 2.6e+140) {
		tmp = fma(c, b, (-4.0 * (a * t))) - ((j * 27.0) * k);
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -8e+23)
		tmp = Float64(fma(Float64(Float64(t * z) * 18.0), y, Float64(-4.0 * i)) * x);
	elseif (x <= 2.6e+140)
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -8e+23], N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.6e+140], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.9999999999999993e23

   1. Initial program 75.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 63.5

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

   4. Applied rewrites 63.5%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 64.0

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

   6. Applied rewrites 64.0%

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

   if -7.9999999999999993e23 < x < 2.6000000000000001e140

   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. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 73.7

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

   4. Applied rewrites 73.7%

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

   if 2.6000000000000001e140 < x

   1. Initial program 71.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 71.9

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

   4. Applied rewrites 71.9%

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

Alternative 7: 58.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot x\right) \cdot y, 18, -4 \cdot a\right) \cdot t\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-164}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+81}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

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 -1.3e+20)
   (* (fma (* (* z x) y) 18.0 (* -4.0 a)) t)
   (if (<= t -3.15e-164)
     (- (* c b) (* j (* k 27.0)))
     (if (<= t 1.35e+81)
       (- (* (* -4.0 i) x) (* (* j 27.0) k))
       (* (fma (* (* y x) z) 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 <= -1.3e+20) {
		tmp = fma(((z * x) * y), 18.0, (-4.0 * a)) * t;
	} else if (t <= -3.15e-164) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t <= 1.35e+81) {
		tmp = ((-4.0 * i) * x) - ((j * 27.0) * k);
	} else {
		tmp = fma(((y * x) * z), 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 <= -1.3e+20)
		tmp = Float64(fma(Float64(Float64(z * x) * y), 18.0, Float64(-4.0 * a)) * t);
	elseif (t <= -3.15e-164)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t <= 1.35e+81)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(Float64(y * x) * z), 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, -1.3e+20], N[(N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -3.15e-164], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+81], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3e20

   1. Initial program 84.2%

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

   2. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 90.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 90.9

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

   6. Applied rewrites 90.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 90.5

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

   8. Applied rewrites 90.5%

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

   9. Taylor expanded in t around inf

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

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

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

       2. metadata-eval N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. +-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. associate-*r* N/A

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

       11. *-commutative N/A

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

       12. lower-*.f64 N/A

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

       13. lift-*.f64 N/A

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

       14. lift-*.f64 64.6

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

   11. Applied rewrites 64.6%

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

   if -1.3e20 < t < -3.15000000000000004e-164

   1. Initial program 89.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 50.7

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

   4. Applied rewrites 50.7%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 50.7

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

   6. Applied rewrites 50.7%

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

   if -3.15000000000000004e-164 < t < 1.35e81

   1. Initial program 85.9%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 53.1

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

   4. Applied rewrites 53.1%

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

   if 1.35e81 < t

   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. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 88.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 88.4

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

   6. Applied rewrites 88.4%

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

   7. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 70.4

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

   9. Applied rewrites 70.4%

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

Alternative 8: 58.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-164}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+81}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* (* y x) z) 18.0 (* -4.0 a)) t)))
   (if (<= t -5.5e+16)
     t_1
     (if (<= t -3.15e-164)
       (- (* c b) (* j (* k 27.0)))
       (if (<= t 1.35e+81) (- (* (* -4.0 i) x) (* (* j 27.0) k)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(((y * x) * z), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -5.5e+16) {
		tmp = t_1;
	} else if (t <= -3.15e-164) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t <= 1.35e+81) {
		tmp = ((-4.0 * i) * x) - ((j * 27.0) * k);
	} 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(fma(Float64(Float64(y * x) * z), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -5.5e+16)
		tmp = t_1;
	elseif (t <= -3.15e-164)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t <= 1.35e+81)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.5e+16], t$95$1, If[LessEqual[t, -3.15e-164], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+81], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5e16 or 1.35e81 < t

   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. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 89.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 89.8

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

   6. Applied rewrites 89.8%

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

   7. Taylor expanded in t around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 67.2

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

   9. Applied rewrites 67.2%

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

   if -5.5e16 < t < -3.15000000000000004e-164

   1. Initial program 89.3%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 50.6

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

   4. Applied rewrites 50.6%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 50.7

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

   6. Applied rewrites 50.7%

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

   if -3.15000000000000004e-164 < t < 1.35e81

   1. Initial program 85.9%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 53.1

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

   4. Applied rewrites 53.1%

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

Alternative 9: 57.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+23}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - t\_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)) (t_2 (* (* j 27.0) k)))
   (if (<= x -7.8e+92)
     t_1
     (if (<= x -5.6e+23)
       (- (* (* -4.0 i) x) t_2)
       (if (<= x 4.5e-43) (- (* -4.0 (* a t)) t_2) 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((18.0 * t), (z * y), (-4.0 * i)) * x;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (x <= -7.8e+92) {
		tmp = t_1;
	} else if (x <= -5.6e+23) {
		tmp = ((-4.0 * i) * x) - t_2;
	} else if (x <= 4.5e-43) {
		tmp = (-4.0 * (a * t)) - t_2;
	} 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(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -7.8e+92)
		tmp = t_1;
	elseif (x <= -5.6e+23)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - t_2);
	elseif (x <= 4.5e-43)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - t_2);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -7.8e+92], t$95$1, If[LessEqual[x, -5.6e+23], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[x, 4.5e-43], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000022e92 or 4.50000000000000025e-43 < x

   1. Initial program 75.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 62.6

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

   4. Applied rewrites 62.6%

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

   if -7.80000000000000022e92 < x < -5.6e23

   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. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 46.6

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

   4. Applied rewrites 46.6%

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

   if -5.6e23 < x < 4.50000000000000025e-43

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 53.4

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

   4. Applied rewrites 53.4%

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

Alternative 10: 55.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -5.8e-111)
   (* (fma (* (* t z) 18.0) y (* -4.0 i)) x)
   (if (<= x 4.5e-43)
     (- (* -4.0 (* a t)) (* (* j 27.0) k))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -5.8e-111) {
		tmp = fma(((t * z) * 18.0), y, (-4.0 * i)) * x;
	} else if (x <= 4.5e-43) {
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * k);
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -5.8e-111)
		tmp = Float64(fma(Float64(Float64(t * z) * 18.0), y, Float64(-4.0 * i)) * x);
	elseif (x <= 4.5e-43)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -5.8e-111], N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 4.5e-43], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.80000000000000003e-111

   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. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 53.1

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

   4. Applied rewrites 53.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 54.0

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

   6. Applied rewrites 54.0%

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

   if -5.80000000000000003e-111 < x < 4.50000000000000025e-43

   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. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 55.6

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

   4. Applied rewrites 55.6%

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

   if 4.50000000000000025e-43 < x

   1. Initial program 77.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 58.6

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

   4. Applied rewrites 58.6%

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

Alternative 11: 55.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot \left(z \cdot 18\right), y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-43}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -5.8e-111)
   (* (fma (* t (* z 18.0)) y (* -4.0 i)) x)
   (if (<= x 4.5e-43)
     (- (* -4.0 (* a t)) (* (* j 27.0) k))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -5.8e-111) {
		tmp = fma((t * (z * 18.0)), y, (-4.0 * i)) * x;
	} else if (x <= 4.5e-43) {
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * k);
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -5.8e-111)
		tmp = Float64(fma(Float64(t * Float64(z * 18.0)), y, Float64(-4.0 * i)) * x);
	elseif (x <= 4.5e-43)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -5.8e-111], N[(N[(N[(t * N[(z * 18.0), $MachinePrecision]), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 4.5e-43], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.80000000000000003e-111

   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. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 53.1

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

   4. Applied rewrites 53.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 54.0

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

   6. Applied rewrites 54.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 54.1

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

   8. Applied rewrites 54.1%

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

   if -5.80000000000000003e-111 < x < 4.50000000000000025e-43

   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. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 55.6

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

   4. Applied rewrites 55.6%

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

   if 4.50000000000000025e-43 < x

   1. Initial program 77.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 58.6

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

   4. Applied rewrites 58.6%

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

Alternative 12: 48.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(-4 \cdot i\right) \cdot x - t\_1\\ \mathbf{if}\;i \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{-23}:\\ \;\;\;\;\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+16}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (* (* -4.0 i) x) t_1)))
   (if (<= i -3.3e+103)
     t_2
     (if (<= i -3.9e-23)
       (* (* (* (* y x) z) t) 18.0)
       (if (<= i 2.9e+16) (- (* -4.0 (* a t)) t_1) t_2)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((-4.0 * i) * x) - t_1;
	double tmp;
	if (i <= -3.3e+103) {
		tmp = t_2;
	} else if (i <= -3.9e-23) {
		tmp = (((y * x) * z) * t) * 18.0;
	} else if (i <= 2.9e+16) {
		tmp = (-4.0 * (a * t)) - t_1;
	} else {
		tmp = t_2;
	}
	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 = (j * 27.0d0) * k
    t_2 = (((-4.0d0) * i) * x) - t_1
    if (i <= (-3.3d+103)) then
        tmp = t_2
    else if (i <= (-3.9d-23)) then
        tmp = (((y * x) * z) * t) * 18.0d0
    else if (i <= 2.9d+16) then
        tmp = ((-4.0d0) * (a * t)) - t_1
    else
        tmp = t_2
    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 t_2 = ((-4.0 * i) * x) - t_1;
	double tmp;
	if (i <= -3.3e+103) {
		tmp = t_2;
	} else if (i <= -3.9e-23) {
		tmp = (((y * x) * z) * t) * 18.0;
	} else if (i <= 2.9e+16) {
		tmp = (-4.0 * (a * t)) - t_1;
	} else {
		tmp = t_2;
	}
	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
	t_2 = ((-4.0 * i) * x) - t_1
	tmp = 0
	if i <= -3.3e+103:
		tmp = t_2
	elif i <= -3.9e-23:
		tmp = (((y * x) * z) * t) * 18.0
	elif i <= 2.9e+16:
		tmp = (-4.0 * (a * t)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(-4.0 * i) * x) - t_1)
	tmp = 0.0
	if (i <= -3.3e+103)
		tmp = t_2;
	elseif (i <= -3.9e-23)
		tmp = Float64(Float64(Float64(Float64(y * x) * z) * t) * 18.0);
	elseif (i <= 2.9e+16)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - t_1);
	else
		tmp = t_2;
	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;
	t_2 = ((-4.0 * i) * x) - t_1;
	tmp = 0.0;
	if (i <= -3.3e+103)
		tmp = t_2;
	elseif (i <= -3.9e-23)
		tmp = (((y * x) * z) * t) * 18.0;
	elseif (i <= 2.9e+16)
		tmp = (-4.0 * (a * t)) - t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[i, -3.3e+103], t$95$2, If[LessEqual[i, -3.9e-23], N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[i, 2.9e+16], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.30000000000000009e103 or 2.9e16 < i

   1. Initial program 82.3%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 55.2

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

   4. Applied rewrites 55.2%

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

   if -3.30000000000000009e103 < i < -3.9e-23

   1. Initial program 85.0%

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

   2. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 87.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 87.8

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

   6. Applied rewrites 87.8%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 26.6

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

   9. Applied rewrites 26.6%

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

   if -3.9e-23 < i < 2.9e16

   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. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 47.5

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

   4. Applied rewrites 47.5%

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

Alternative 13: 47.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;t\_1 \leq 10^{+168}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+234}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 -2e+305)
     (* (* (* (* y x) z) t) 18.0)
     (if (<= t_1 1e+168)
       (- (* c b) (* j (* k 27.0)))
       (if (<= t_1 1e+234)
         (* (* -4.0 i) x)
         (if (<= t_1 5e+298)
           (* -4.0 (* a t))
           (* (* (* (* t y) 18.0) z) x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = (((y * x) * z) * t) * 18.0;
	} else if (t_1 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_1 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_1 <= 5e+298) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= (-2d+305)) then
        tmp = (((y * x) * z) * t) * 18.0d0
    else if (t_1 <= 1d+168) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else if (t_1 <= 1d+234) then
        tmp = ((-4.0d0) * i) * x
    else if (t_1 <= 5d+298) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = (((t * y) * 18.0d0) * z) * x
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = (((y * x) * z) * t) * 18.0;
	} else if (t_1 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_1 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_1 <= 5e+298) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -2e+305:
		tmp = (((y * x) * z) * t) * 18.0
	elif t_1 <= 1e+168:
		tmp = (c * b) - (j * (k * 27.0))
	elif t_1 <= 1e+234:
		tmp = (-4.0 * i) * x
	elif t_1 <= 5e+298:
		tmp = -4.0 * (a * t)
	else:
		tmp = (((t * y) * 18.0) * z) * x
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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 <= -2e+305)
		tmp = Float64(Float64(Float64(Float64(y * x) * z) * t) * 18.0);
	elseif (t_1 <= 1e+168)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 1e+234)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (t_1 <= 5e+298)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * z) * x);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -2e+305)
		tmp = (((y * x) * z) * t) * 18.0;
	elseif (t_1 <= 1e+168)
		tmp = (c * b) - (j * (k * 27.0));
	elseif (t_1 <= 1e+234)
		tmp = (-4.0 * i) * x;
	elseif (t_1 <= 5e+298)
		tmp = -4.0 * (a * t);
	else
		tmp = (((t * y) * 18.0) * z) * x;
	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[(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, -2e+305], N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+168], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+234], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 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)) < -1.9999999999999999e305

   1. Initial program 83.6%

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

   2. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 86.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 83.7

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

   6. Applied rewrites 83.7%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 39.6

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

   9. Applied rewrites 39.6%

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

   if -1.9999999999999999e305 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 9.9999999999999993e167

   1. Initial program 99.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.7

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

   4. Applied rewrites 57.7%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 57.8

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

   6. Applied rewrites 57.8%

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

   if 9.9999999999999993e167 < (-.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)) < 1.00000000000000002e234

   1. Initial program 99.6%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 20.0

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

   4. Applied rewrites 20.0%

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

   if 1.00000000000000002e234 < (-.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)) < 5.0000000000000003e298

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 25.1

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

   4. Applied rewrites 25.1%

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

   if 5.0000000000000003e298 < (-.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 59.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 61.5

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

   7. Applied rewrites 61.5%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 44.0

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

   10. Applied rewrites 44.0%

       \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 14: 47.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot \left(t \cdot 18\right)\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 10^{+168}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+234}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 -2e+305)
     (* (* (* z y) (* t 18.0)) x)
     (if (<= t_1 1e+168)
       (- (* c b) (* j (* k 27.0)))
       (if (<= t_1 1e+234)
         (* (* -4.0 i) x)
         (if (<= t_1 5e+298)
           (* -4.0 (* a t))
           (* (* (* (* t y) 18.0) z) x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = ((z * y) * (t * 18.0)) * x;
	} else if (t_1 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_1 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_1 <= 5e+298) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= (-2d+305)) then
        tmp = ((z * y) * (t * 18.0d0)) * x
    else if (t_1 <= 1d+168) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else if (t_1 <= 1d+234) then
        tmp = ((-4.0d0) * i) * x
    else if (t_1 <= 5d+298) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = (((t * y) * 18.0d0) * z) * x
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = ((z * y) * (t * 18.0)) * x;
	} else if (t_1 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_1 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_1 <= 5e+298) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -2e+305:
		tmp = ((z * y) * (t * 18.0)) * x
	elif t_1 <= 1e+168:
		tmp = (c * b) - (j * (k * 27.0))
	elif t_1 <= 1e+234:
		tmp = (-4.0 * i) * x
	elif t_1 <= 5e+298:
		tmp = -4.0 * (a * t)
	else:
		tmp = (((t * y) * 18.0) * z) * x
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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 <= -2e+305)
		tmp = Float64(Float64(Float64(z * y) * Float64(t * 18.0)) * x);
	elseif (t_1 <= 1e+168)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 1e+234)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (t_1 <= 5e+298)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * z) * x);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -2e+305)
		tmp = ((z * y) * (t * 18.0)) * x;
	elseif (t_1 <= 1e+168)
		tmp = (c * b) - (j * (k * 27.0));
	elseif (t_1 <= 1e+234)
		tmp = (-4.0 * i) * x;
	elseif (t_1 <= 5e+298)
		tmp = -4.0 * (a * t);
	else
		tmp = (((t * y) * 18.0) * z) * x;
	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[(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, -2e+305], N[(N[(N[(z * y), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1e+168], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+234], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 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)) < -1.9999999999999999e305

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 55.5

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

   4. Applied rewrites 55.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 40.3

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

   7. Applied rewrites 40.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 40.3

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

   9. Applied rewrites 40.3%

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

   if -1.9999999999999999e305 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 9.9999999999999993e167

   1. Initial program 99.6%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.7

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

   4. Applied rewrites 57.7%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 57.8

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

   6. Applied rewrites 57.8%

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

   if 9.9999999999999993e167 < (-.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)) < 1.00000000000000002e234

   1. Initial program 99.6%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 20.0

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

   4. Applied rewrites 20.0%

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

   if 1.00000000000000002e234 < (-.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)) < 5.0000000000000003e298

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 25.1

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

   4. Applied rewrites 25.1%

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

   if 5.0000000000000003e298 < (-.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 59.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 59.8

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

   4. Applied rewrites 59.8%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 61.5

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

   7. Applied rewrites 61.5%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 44.0

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

   10. Applied rewrites 44.0%

       \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 15: 47.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 10^{+168}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+234}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 -2e+305)
     (* (* (* t (* y 18.0)) z) x)
     (if (<= t_1 1e+168)
       (- (* c b) (* j (* k 27.0)))
       (if (<= t_1 1e+234)
         (* (* -4.0 i) x)
         (if (<= t_1 5e+298)
           (* -4.0 (* a t))
           (* (* (* (* t y) 18.0) z) x)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = ((t * (y * 18.0)) * z) * x;
	} else if (t_1 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_1 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_1 <= 5e+298) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= (-2d+305)) then
        tmp = ((t * (y * 18.0d0)) * z) * x
    else if (t_1 <= 1d+168) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else if (t_1 <= 1d+234) then
        tmp = ((-4.0d0) * i) * x
    else if (t_1 <= 5d+298) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = (((t * y) * 18.0d0) * z) * x
    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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -2e+305) {
		tmp = ((t * (y * 18.0)) * z) * x;
	} else if (t_1 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_1 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_1 <= 5e+298) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -2e+305:
		tmp = ((t * (y * 18.0)) * z) * x
	elif t_1 <= 1e+168:
		tmp = (c * b) - (j * (k * 27.0))
	elif t_1 <= 1e+234:
		tmp = (-4.0 * i) * x
	elif t_1 <= 5e+298:
		tmp = -4.0 * (a * t)
	else:
		tmp = (((t * y) * 18.0) * z) * x
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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 <= -2e+305)
		tmp = Float64(Float64(Float64(t * Float64(y * 18.0)) * z) * x);
	elseif (t_1 <= 1e+168)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 1e+234)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (t_1 <= 5e+298)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * z) * x);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -2e+305)
		tmp = ((t * (y * 18.0)) * z) * x;
	elseif (t_1 <= 1e+168)
		tmp = (c * b) - (j * (k * 27.0));
	elseif (t_1 <= 1e+234)
		tmp = (-4.0 * i) * x;
	elseif (t_1 <= 5e+298)
		tmp = -4.0 * (a * t);
	else
		tmp = (((t * y) * 18.0) * z) * x;
	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[(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, -2e+305], N[(N[(N[(t * N[(y * 18.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1e+168], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+234], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 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)) < -1.9999999999999999e305

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 55.5

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

   4. Applied rewrites 55.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right) + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18 + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      9. lower-/.f64 58.8

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   7. Applied rewrites 58.8%

      \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   8. Taylor expanded in y around inf

      \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      3. lift-*.f64 42.2

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

   10. Applied rewrites 42.2%

       \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

       2. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

       3. associate-*l* N/A

          \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

       4. *-commutative N/A

          \[\leadsto \left(\left(t \cdot \left(18 \cdot y\right)\right) \cdot z\right) \cdot x \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\left(t \cdot \left(18 \cdot y\right)\right) \cdot z\right) \cdot x \]

       6. *-commutative N/A

          \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

       7. lower-*.f64 42.2

          \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

   12. Applied rewrites 42.2%

       \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

   if -1.9999999999999999e305 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 9.9999999999999993e167

   1. Initial program 99.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 57.7

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 57.7%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

         \[\leadsto c \cdot b - \color{blue}{j \cdot \left(27 \cdot k\right)} \]

      5. *-commutative N/A

         \[\leadsto c \cdot b - j \cdot \color{blue}{\left(k \cdot 27\right)} \]

      6. lower-*.f64 57.8

         \[\leadsto c \cdot b - j \cdot \color{blue}{\left(k \cdot 27\right)} \]

   6. Applied rewrites 57.8%

      \[\leadsto c \cdot b - \color{blue}{j \cdot \left(k \cdot 27\right)} \]

   if 9.9999999999999993e167 < (-.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)) < 1.00000000000000002e234

   1. Initial program 99.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 20.0

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   4. Applied rewrites 20.0%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

   if 1.00000000000000002e234 < (-.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)) < 5.0000000000000003e298

   1. Initial program 99.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 25.1

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 25.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if 5.0000000000000003e298 < (-.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 59.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + -4 \cdot i\right) \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 59.8

          \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right) + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18 + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      9. lower-/.f64 61.5

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   7. Applied rewrites 61.5%

      \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   8. Taylor expanded in y around inf

      \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      3. lift-*.f64 44.0

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

   10. Applied rewrites 44.0%

       \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 46.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x\\ t_2 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+168}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+234}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* t (* y 18.0)) z) x))
        (t_2
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_2 -2e+305)
     t_1
     (if (<= t_2 1e+168)
       (- (* c b) (* j (* k 27.0)))
       (if (<= t_2 1e+234)
         (* (* -4.0 i) x)
         (if (<= t_2 5e+298) (* -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 = ((t * (y * 18.0)) * z) * x;
	double t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_2 <= -2e+305) {
		tmp = t_1;
	} else if (t_2 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_2 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_2 <= 5e+298) {
		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 = ((t * (y * 18.0d0)) * z) * x
    t_2 = ((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)
    if (t_2 <= (-2d+305)) then
        tmp = t_1
    else if (t_2 <= 1d+168) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else if (t_2 <= 1d+234) then
        tmp = ((-4.0d0) * i) * x
    else if (t_2 <= 5d+298) 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 = ((t * (y * 18.0)) * z) * x;
	double t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_2 <= -2e+305) {
		tmp = t_1;
	} else if (t_2 <= 1e+168) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t_2 <= 1e+234) {
		tmp = (-4.0 * i) * x;
	} else if (t_2 <= 5e+298) {
		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 = ((t * (y * 18.0)) * z) * x
	t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_2 <= -2e+305:
		tmp = t_1
	elif t_2 <= 1e+168:
		tmp = (c * b) - (j * (k * 27.0))
	elif t_2 <= 1e+234:
		tmp = (-4.0 * i) * x
	elif t_2 <= 5e+298:
		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(Float64(Float64(t * Float64(y * 18.0)) * z) * x)
	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))
	tmp = 0.0
	if (t_2 <= -2e+305)
		tmp = t_1;
	elseif (t_2 <= 1e+168)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t_2 <= 1e+234)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (t_2 <= 5e+298)
		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 = ((t * (y * 18.0)) * z) * x;
	t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_2 <= -2e+305)
		tmp = t_1;
	elseif (t_2 <= 1e+168)
		tmp = (c * b) - (j * (k * 27.0));
	elseif (t_2 <= 1e+234)
		tmp = (-4.0 * i) * x;
	elseif (t_2 <= 5e+298)
		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[(N[(N[(t * N[(y * 18.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] * x), $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]}, If[LessEqual[t$95$2, -2e+305], t$95$1, If[LessEqual[t$95$2, 1e+168], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+234], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 5e+298], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 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)) < -1.9999999999999999e305 or 5.0000000000000003e298 < (-.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 69.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + -4 \cdot i\right) \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 58.0

          \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

   4. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right) + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18 + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      9. lower-/.f64 60.4

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   7. Applied rewrites 60.4%

      \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   8. Taylor expanded in y around inf

      \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      3. lift-*.f64 43.2

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

   10. Applied rewrites 43.2%

       \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

       2. lift-*.f64 N/A

          \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

       3. associate-*l* N/A

          \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

       4. *-commutative N/A

          \[\leadsto \left(\left(t \cdot \left(18 \cdot y\right)\right) \cdot z\right) \cdot x \]

       5. lower-*.f64 N/A

          \[\leadsto \left(\left(t \cdot \left(18 \cdot y\right)\right) \cdot z\right) \cdot x \]

       6. *-commutative N/A

          \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

       7. lower-*.f64 43.2

          \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

   12. Applied rewrites 43.2%

       \[\leadsto \left(\left(t \cdot \left(y \cdot 18\right)\right) \cdot z\right) \cdot x \]

   if -1.9999999999999999e305 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 9.9999999999999993e167

   1. Initial program 99.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 57.7

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 57.7%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

         \[\leadsto c \cdot b - \color{blue}{j \cdot \left(27 \cdot k\right)} \]

      5. *-commutative N/A

         \[\leadsto c \cdot b - j \cdot \color{blue}{\left(k \cdot 27\right)} \]

      6. lower-*.f64 57.8

         \[\leadsto c \cdot b - j \cdot \color{blue}{\left(k \cdot 27\right)} \]

   6. Applied rewrites 57.8%

      \[\leadsto c \cdot b - \color{blue}{j \cdot \left(k \cdot 27\right)} \]

   if 9.9999999999999993e167 < (-.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)) < 1.00000000000000002e234

   1. Initial program 99.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 20.0

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   4. Applied rewrites 20.0%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

   if 1.00000000000000002e234 < (-.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)) < 5.0000000000000003e298

   1. Initial program 99.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 25.1

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 25.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 46.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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 (- INFINITY))
     (* (* (* (* y x) z) t) 18.0)
     (if (<= t_1 5e+298)
       (- (* -4.0 (* a t)) (* (* j 27.0) k))
       (* (* (* (* t y) 18.0) z) x)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((y * x) * z) * t) * 18.0;
	} else if (t_1 <= 5e+298) {
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * k);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	return tmp;
}

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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((y * x) * z) * t) * 18.0;
	} else if (t_1 <= 5e+298) {
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * k);
	} else {
		tmp = (((t * y) * 18.0) * z) * x;
	}
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((y * x) * z) * t) * 18.0
	elif t_1 <= 5e+298:
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * k)
	else:
		tmp = (((t * y) * 18.0) * z) * x
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(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 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(y * x) * z) * t) * 18.0);
	elseif (t_1 <= 5e+298)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(Float64(t * y) * 18.0) * z) * x);
	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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((y * x) * z) * t) * 18.0;
	elseif (t_1 <= 5e+298)
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * k);
	else
		tmp = (((t * y) * 18.0) * z) * x;
	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[(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, (-Infinity)], N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+298], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision] * x), $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)) < -inf.0

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(i \cdot x\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(-4 \cdot \left(i \cdot x\right) + \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(\color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - 4 \cdot \left(a \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \color{blue}{\left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      4. metadata-eval N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(\color{blue}{a} \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. +-commutative N/A

         \[\leadsto \left(\left(-4 \cdot i\right) \cdot x + \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, \color{blue}{x}, -4 \cdot \left(a \cdot t\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, -4 \cdot \left(a \cdot t\right) + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \left(-4 \cdot a\right) \cdot t + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t, 18, c \cdot b\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot x\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(x \cdot y\right) \cdot z\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. lower-*.f64 83.5

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

   6. Applied rewrites 83.5%

      \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t, 18, c \cdot b\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot \color{blue}{18} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot \color{blue}{18} \]

      3. associate-*r* N/A

         \[\leadsto \left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right) \cdot 18 \]

      4. *-commutative N/A

         \[\leadsto \left(t \cdot \left(\left(y \cdot x\right) \cdot z\right)\right) \cdot 18 \]

      5. *-commutative N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

      8. lift-*.f64 39.7

         \[\leadsto \left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18 \]

   9. Applied rewrites 39.7%

      \[\leadsto \color{blue}{\left(\left(\left(y \cdot x\right) \cdot z\right) \cdot t\right) \cdot 18} \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 5.0000000000000003e298

   1. Initial program 99.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 52.9

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 52.9%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   if 5.0000000000000003e298 < (-.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 59.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) \cdot \color{blue}{x} \]

      3. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + -4 \cdot i\right) \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, y \cdot z, -4 \cdot i\right) \cdot x \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

      10. lower-*.f64 59.8

          \[\leadsto \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x \]

   4. Applied rewrites 59.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(z \cdot \left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(-4 \cdot \frac{i}{z} + 18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right) + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18 + -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, -4 \cdot \frac{i}{z}\right) \cdot z\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

      9. lower-/.f64 61.5

         \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   7. Applied rewrites 61.5%

      \[\leadsto \left(\mathsf{fma}\left(t \cdot y, 18, \frac{i}{z} \cdot -4\right) \cdot z\right) \cdot x \]

   8. Taylor expanded in y around inf

      \[\leadsto \left(\left(18 \cdot \left(t \cdot y\right)\right) \cdot z\right) \cdot x \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

      3. lift-*.f64 44.0

         \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]

   10. Applied rewrites 44.0%

       \[\leadsto \left(\left(\left(t \cdot y\right) \cdot 18\right) \cdot z\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 45.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+35}:\\ \;\;\;\;c \cdot b - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= t -2.35e+30)
     t_1
     (if (<= t 7.6e+35)
       (- (* c b) (* (* j 27.0) k))
       (if (<= t 3.8e+151) (* (* -4.0 i) x) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (t <= -2.35e+30) {
		tmp = t_1;
	} else if (t <= 7.6e+35) {
		tmp = (c * b) - ((j * 27.0) * k);
	} else if (t <= 3.8e+151) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (t <= (-2.35d+30)) then
        tmp = t_1
    else if (t <= 7.6d+35) then
        tmp = (c * b) - ((j * 27.0d0) * k)
    else if (t <= 3.8d+151) then
        tmp = ((-4.0d0) * i) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (t <= -2.35e+30) {
		tmp = t_1;
	} else if (t <= 7.6e+35) {
		tmp = (c * b) - ((j * 27.0) * k);
	} else if (t <= 3.8e+151) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if t <= -2.35e+30:
		tmp = t_1
	elif t <= 7.6e+35:
		tmp = (c * b) - ((j * 27.0) * k)
	elif t <= 3.8e+151:
		tmp = (-4.0 * i) * x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (t <= -2.35e+30)
		tmp = t_1;
	elseif (t <= 7.6e+35)
		tmp = Float64(Float64(c * b) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 3.8e+151)
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (t <= -2.35e+30)
		tmp = t_1;
	elseif (t <= 7.6e+35)
		tmp = (c * b) - ((j * 27.0) * k);
	elseif (t <= 3.8e+151)
		tmp = (-4.0 * i) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e+30], t$95$1, If[LessEqual[t, 7.6e+35], N[(N[(c * b), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+151], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.34999999999999995e30 or 3.8e151 < t

   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. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 37.5

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 37.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if -2.34999999999999995e30 < t < 7.5999999999999999e35

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 55.5

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 55.5%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]

   if 7.5999999999999999e35 < t < 3.8e151

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 15.1

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   4. Applied rewrites 15.1%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 45.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+35}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= t -2.35e+30)
     t_1
     (if (<= t 7.6e+35)
       (- (* c b) (* j (* k 27.0)))
       (if (<= t 3.8e+151) (* (* -4.0 i) x) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (t <= -2.35e+30) {
		tmp = t_1;
	} else if (t <= 7.6e+35) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t <= 3.8e+151) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (t <= (-2.35d+30)) then
        tmp = t_1
    else if (t <= 7.6d+35) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else if (t <= 3.8d+151) then
        tmp = ((-4.0d0) * i) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (t <= -2.35e+30) {
		tmp = t_1;
	} else if (t <= 7.6e+35) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t <= 3.8e+151) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if t <= -2.35e+30:
		tmp = t_1
	elif t <= 7.6e+35:
		tmp = (c * b) - (j * (k * 27.0))
	elif t <= 3.8e+151:
		tmp = (-4.0 * i) * x
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (t <= -2.35e+30)
		tmp = t_1;
	elseif (t <= 7.6e+35)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t <= 3.8e+151)
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (t <= -2.35e+30)
		tmp = t_1;
	elseif (t <= 7.6e+35)
		tmp = (c * b) - (j * (k * 27.0));
	elseif (t <= 3.8e+151)
		tmp = (-4.0 * i) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e+30], t$95$1, If[LessEqual[t, 7.6e+35], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+151], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.34999999999999995e30 or 3.8e151 < t

   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. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 37.5

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 37.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if -2.34999999999999995e30 < t < 7.5999999999999999e35

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 55.5

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 55.5%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
   5. 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. lower-*.f64 N/A

         \[\leadsto c \cdot b - \color{blue}{j \cdot \left(27 \cdot k\right)} \]

      5. *-commutative N/A

         \[\leadsto c \cdot b - j \cdot \color{blue}{\left(k \cdot 27\right)} \]

      6. lower-*.f64 55.6

         \[\leadsto c \cdot b - j \cdot \color{blue}{\left(k \cdot 27\right)} \]

   6. Applied rewrites 55.6%

      \[\leadsto c \cdot b - \color{blue}{j \cdot \left(k \cdot 27\right)} \]

   if 7.5999999999999999e35 < t < 3.8e151

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 15.1

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   4. Applied rewrites 15.1%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+172}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+137}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_1 \leq 20000000:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+172)
     (* (* -27.0 k) j)
     (if (<= t_1 -4e+137)
       (* c b)
       (if (<= t_1 20000000.0) (* (* -4.0 i) x) (* (* -27.0 j) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+172) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= -4e+137) {
		tmp = c * b;
	} else if (t_1 <= 20000000.0) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+172)) then
        tmp = ((-27.0d0) * k) * j
    else if (t_1 <= (-4d+137)) then
        tmp = c * b
    else if (t_1 <= 20000000.0d0) then
        tmp = ((-4.0d0) * i) * x
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+172) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= -4e+137) {
		tmp = c * b;
	} else if (t_1 <= 20000000.0) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+172:
		tmp = (-27.0 * k) * j
	elif t_1 <= -4e+137:
		tmp = c * b
	elif t_1 <= 20000000.0:
		tmp = (-4.0 * i) * x
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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+172)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (t_1 <= -4e+137)
		tmp = Float64(c * b);
	elseif (t_1 <= 20000000.0)
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+172)
		tmp = (-27.0 * k) * j;
	elseif (t_1 <= -4e+137)
		tmp = c * b;
	elseif (t_1 <= 20000000.0)
		tmp = (-4.0 * i) * x;
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+172], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, -4e+137], N[(c * b), $MachinePrecision], If[LessEqual[t$95$1, 20000000.0], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000002e172

   1. Initial program 79.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 65.7

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 65.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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 65.7

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

   6. Applied rewrites 65.7%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

   if -2.0000000000000002e172 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000001e137

   1. Initial program 85.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 25.8

         \[\leadsto c \cdot \color{blue}{b} \]

   4. Applied rewrites 25.8%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.0000000000000001e137 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e7

   1. Initial program 87.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot \color{blue}{x} \]

      3. lower-*.f64 24.4

         \[\leadsto \left(-4 \cdot i\right) \cdot x \]

   4. Applied rewrites 24.4%

      \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

   if 2e7 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 81.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 45.3

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 45.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      6. lower-*.f64 45.3

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   6. Applied rewrites 45.3%

      \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 21: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+172}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-71}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_1 \leq 10^{+81}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+172)
     (* (* -27.0 k) j)
     (if (<= t_1 -5e-71)
       (* c b)
       (if (<= t_1 1e+81) (* -4.0 (* a t)) (* (* -27.0 j) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+172) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= -5e-71) {
		tmp = c * b;
	} else if (t_1 <= 1e+81) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+172)) then
        tmp = ((-27.0d0) * k) * j
    else if (t_1 <= (-5d-71)) then
        tmp = c * b
    else if (t_1 <= 1d+81) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+172) {
		tmp = (-27.0 * k) * j;
	} else if (t_1 <= -5e-71) {
		tmp = c * b;
	} else if (t_1 <= 1e+81) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+172:
		tmp = (-27.0 * k) * j
	elif t_1 <= -5e-71:
		tmp = c * b
	elif t_1 <= 1e+81:
		tmp = -4.0 * (a * t)
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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+172)
		tmp = Float64(Float64(-27.0 * k) * j);
	elseif (t_1 <= -5e-71)
		tmp = Float64(c * b);
	elseif (t_1 <= 1e+81)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+172)
		tmp = (-27.0 * k) * j;
	elseif (t_1 <= -5e-71)
		tmp = c * b;
	elseif (t_1 <= 1e+81)
		tmp = -4.0 * (a * t);
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+172], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[t$95$1, -5e-71], N[(c * b), $MachinePrecision], If[LessEqual[t$95$1, 1e+81], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000002e172

   1. Initial program 79.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 65.7

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 65.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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 65.7

         \[\leadsto \left(-27 \cdot k\right) \cdot j \]

   6. Applied rewrites 65.7%

      \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]

   if -2.0000000000000002e172 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999998e-71

   1. Initial program 87.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 25.4

         \[\leadsto c \cdot \color{blue}{b} \]

   4. Applied rewrites 25.4%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.99999999999999998e-71 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999921e80

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 25.8

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 25.8%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if 9.99999999999999921e80 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 54.6

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 54.6%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      6. lower-*.f64 54.6

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   6. Applied rewrites 54.6%

      \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 22: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+172}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-71}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_1 \leq 10^{+81}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+172)
     (* -27.0 (* k j))
     (if (<= t_1 -5e-71)
       (* c b)
       (if (<= t_1 1e+81) (* -4.0 (* a t)) (* (* -27.0 j) k))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+172) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= -5e-71) {
		tmp = c * b;
	} else if (t_1 <= 1e+81) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+172)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= (-5d-71)) then
        tmp = c * b
    else if (t_1 <= 1d+81) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+172) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= -5e-71) {
		tmp = c * b;
	} else if (t_1 <= 1e+81) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+172:
		tmp = -27.0 * (k * j)
	elif t_1 <= -5e-71:
		tmp = c * b
	elif t_1 <= 1e+81:
		tmp = -4.0 * (a * t)
	else:
		tmp = (-27.0 * j) * k
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
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+172)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= -5e-71)
		tmp = Float64(c * b);
	elseif (t_1 <= 1e+81)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+172)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= -5e-71)
		tmp = c * b;
	elseif (t_1 <= 1e+81)
		tmp = -4.0 * (a * t);
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+172], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-71], N[(c * b), $MachinePrecision], If[LessEqual[t$95$1, 1e+81], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000002e172

   1. Initial program 79.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 65.7

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 65.7%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2.0000000000000002e172 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999998e-71

   1. Initial program 87.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 25.4

         \[\leadsto c \cdot \color{blue}{b} \]

   4. Applied rewrites 25.4%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.99999999999999998e-71 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999921e80

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 25.8

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 25.8%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

   if 9.99999999999999921e80 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 54.6

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 54.6%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. 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. *-commutative N/A

         \[\leadsto -27 \cdot \left(j \cdot \color{blue}{k}\right) \]

      4. associate-*r* N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]

      6. lower-*.f64 54.6

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   6. Applied rewrites 54.6%

      \[\leadsto \left(-27 \cdot j\right) \cdot \color{blue}{k} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 23: 36.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-71}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t\_2 \leq 10^{+81}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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+172)
     t_1
     (if (<= t_2 -5e-71) (* c b) (if (<= t_2 1e+81) (* -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+172) {
		tmp = t_1;
	} else if (t_2 <= -5e-71) {
		tmp = c * b;
	} else if (t_2 <= 1e+81) {
		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+172)) then
        tmp = t_1
    else if (t_2 <= (-5d-71)) then
        tmp = c * b
    else if (t_2 <= 1d+81) 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+172) {
		tmp = t_1;
	} else if (t_2 <= -5e-71) {
		tmp = c * b;
	} else if (t_2 <= 1e+81) {
		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+172:
		tmp = t_1
	elif t_2 <= -5e-71:
		tmp = c * b
	elif t_2 <= 1e+81:
		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+172)
		tmp = t_1;
	elseif (t_2 <= -5e-71)
		tmp = Float64(c * b);
	elseif (t_2 <= 1e+81)
		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+172)
		tmp = t_1;
	elseif (t_2 <= -5e-71)
		tmp = c * b;
	elseif (t_2 <= 1e+81)
		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+172], t$95$1, If[LessEqual[t$95$2, -5e-71], N[(c * b), $MachinePrecision], If[LessEqual[t$95$2, 1e+81], 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) < -2.0000000000000002e172 or 9.99999999999999921e80 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 80.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 59.2

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 59.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2.0000000000000002e172 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999998e-71

   1. Initial program 87.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 25.4

         \[\leadsto c \cdot \color{blue}{b} \]

   4. Applied rewrites 25.4%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.99999999999999998e-71 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999921e80

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} \]

      2. lower-*.f64 25.8

         \[\leadsto -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

   4. Applied rewrites 25.8%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 35.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200000:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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+172) t_1 (if (<= t_2 200000.0) (* c b) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (k * j);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+172) {
		tmp = t_1;
	} else if (t_2 <= 200000.0) {
		tmp = c * b;
	} 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+172)) then
        tmp = t_1
    else if (t_2 <= 200000.0d0) then
        tmp = c * b
    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+172) {
		tmp = t_1;
	} else if (t_2 <= 200000.0) {
		tmp = c * b;
	} 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+172:
		tmp = t_1
	elif t_2 <= 200000.0:
		tmp = c * b
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+172)
		tmp = t_1;
	elseif (t_2 <= 200000.0)
		tmp = Float64(c * b);
	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+172)
		tmp = t_1;
	elseif (t_2 <= 200000.0)
		tmp = c * b;
	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+172], t$95$1, If[LessEqual[t$95$2, 200000.0], N[(c * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000002e172 or 2e5 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 80.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 52.3

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   4. Applied rewrites 52.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -2.0000000000000002e172 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e5

   1. Initial program 87.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 28.4

         \[\leadsto c \cdot \color{blue}{b} \]

   4. Applied rewrites 28.4%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 24.2% accurate, 11.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ c \cdot b \end{array} \]

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 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. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto c \cdot \color{blue}{b} \]

   2. lower-*.f64 24.2

      \[\leadsto c \cdot \color{blue}{b} \]

4. Applied rewrites 24.2%

   \[\leadsto \color{blue}{c \cdot b} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))