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

Percentage Accurate: 85.0% → 91.6%

Time: 12.2s

Alternatives: 21

Speedup: 0.5×

• 50.6% 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: 85.0% 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: 91.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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(-18.0, ((t * y) * z), (i * 4.0)) * x);
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.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 95.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 95.3

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

   3. Applied rewrites 95.3%

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

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 60.3

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

   4. Applied rewrites 60.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 61.2

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

   6. Applied rewrites 61.2%

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

Alternative 2: 89.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.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 95.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 93.0

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

   3. Applied rewrites 93.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

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

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 60.3

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

   4. Applied rewrites 60.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 61.2

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

   6. Applied rewrites 61.2%

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

Alternative 3: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := t\_1 \cdot t\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(t\_2, 18, c \cdot b\right)\right) - t\_3\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;\left(\mathsf{fma}\left(-4, a \cdot t, t\_2 \cdot 18\right) - \left(x \cdot 4\right) \cdot i\right) - t\_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x)) (t_2 (* t_1 t)) (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -5e-130)
     (- (fma (* -4.0 a) t (fma t_2 18.0 (* c b))) t_3)
     (if (<= t_3 4e+60)
       (fma (* 18.0 t) t_1 (- (* c b) (* 4.0 (fma a t (* i x)))))
       (if (<= t_3 2e+280)
         (- (- (fma -4.0 (* a t) (* t_2 18.0)) (* (* x 4.0) i)) t_3)
         (- (* -4.0 (* a t)) t_3))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * x;
	double t_2 = t_1 * t;
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -5e-130) {
		tmp = fma((-4.0 * a), t, fma(t_2, 18.0, (c * b))) - t_3;
	} else if (t_3 <= 4e+60) {
		tmp = fma((18.0 * t), t_1, ((c * b) - (4.0 * fma(a, t, (i * x)))));
	} else if (t_3 <= 2e+280) {
		tmp = (fma(-4.0, (a * t), (t_2 * 18.0)) - ((x * 4.0) * i)) - t_3;
	} else {
		tmp = (-4.0 * (a * t)) - t_3;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	t_2 = Float64(t_1 * t)
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -5e-130)
		tmp = Float64(fma(Float64(-4.0 * a), t, fma(t_2, 18.0, Float64(c * b))) - t_3);
	elseif (t_3 <= 4e+60)
		tmp = fma(Float64(18.0 * t), t_1, Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))));
	elseif (t_3 <= 2e+280)
		tmp = Float64(Float64(fma(-4.0, Float64(a * t), Float64(t_2 * 18.0)) - Float64(Float64(x * 4.0) * i)) - t_3);
	else
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - t_3);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-130], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(t$95$2 * 18.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$3, 4e+60], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+280], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision] + N[(t$95$2 * 18.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999996e-130

   1. Initial program 84.6%

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

   2. Taylor expanded in i around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 76.3

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

   4. Applied rewrites 76.3%

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

   if -4.9999999999999996e-130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e60

   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 j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 86.3

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

   4. Applied rewrites 86.3%

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

   if 3.9999999999999998e60 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.0000000000000001e280

   1. Initial program 85.7%

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

   2. Taylor expanded in b around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 74.3

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

   4. Applied rewrites 74.3%

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

   if 2.0000000000000001e280 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 74.2%

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

   2. Taylor expanded in 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 80.6

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

   4. Applied rewrites 80.6%

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

Alternative 4: 80.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(t\_1 \cdot t, 18, c \cdot b\right)\right) - t\_2\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+182}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(\left(z \cdot x\right) \cdot t, 18, \frac{c \cdot b}{y}\right) \cdot y\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a \cdot t\right) \cdot -4 - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x)) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e-130)
     (- (fma (* -4.0 a) t (fma (* t_1 t) 18.0 (* c b))) t_2)
     (if (<= t_2 4e+60)
       (fma (* 18.0 t) t_1 (- (* c b) (* 4.0 (fma a t (* i x)))))
       (if (<= t_2 5e+182)
         (-
          (fma (* -4.0 a) t (* (fma (* (* z x) t) 18.0 (/ (* c b) y)) y))
          t_2)
         (- (- (* (* a t) -4.0) (* (* x 4.0) i)) (* j (* k 27.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (z * y) * x;
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e-130) {
		tmp = fma((-4.0 * a), t, fma((t_1 * t), 18.0, (c * b))) - t_2;
	} else if (t_2 <= 4e+60) {
		tmp = fma((18.0 * t), t_1, ((c * b) - (4.0 * fma(a, t, (i * x)))));
	} else if (t_2 <= 5e+182) {
		tmp = fma((-4.0 * a), t, (fma(((z * x) * t), 18.0, ((c * b) / y)) * y)) - t_2;
	} else {
		tmp = (((a * t) * -4.0) - ((x * 4.0) * i)) - (j * (k * 27.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e-130)
		tmp = Float64(fma(Float64(-4.0 * a), t, fma(Float64(t_1 * t), 18.0, Float64(c * b))) - t_2);
	elseif (t_2 <= 4e+60)
		tmp = fma(Float64(18.0 * t), t_1, Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))));
	elseif (t_2 <= 5e+182)
		tmp = Float64(fma(Float64(-4.0 * a), t, Float64(fma(Float64(Float64(z * x) * t), 18.0, Float64(Float64(c * b) / y)) * y)) - t_2);
	else
		tmp = Float64(Float64(Float64(Float64(a * t) * -4.0) - Float64(Float64(x * 4.0) * i)) - Float64(j * Float64(k * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-130], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(t$95$1 * t), $MachinePrecision] * 18.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 4e+60], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+182], N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(N[(N[(z * x), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(N[(c * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999996e-130

   1. Initial program 84.6%

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

   2. Taylor expanded in i around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 76.3

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

   4. Applied rewrites 76.3%

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

   if -4.9999999999999996e-130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e60

   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 j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 86.3

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

   4. Applied rewrites 86.3%

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

   if 3.9999999999999998e60 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999973e182

   1. Initial program 85.6%

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

   2. Taylor expanded in i around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 74.7

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

   4. Applied rewrites 74.7%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if 4.99999999999999973e182 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 78.8

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

   3. Applied rewrites 78.8%

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

   4. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 74.9

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

   6. Applied rewrites 74.9%

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

Alternative 5: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(t\_1 \cdot t, 18, c \cdot b\right)\right) - t\_2\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-130}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+242}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - t\_2\\ \end{array} \end{array} \]

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 (* (* z y) x))
        (t_2 (* (* j 27.0) k))
        (t_3 (- (fma (* -4.0 a) t (fma (* t_1 t) 18.0 (* c b))) t_2)))
   (if (<= t_2 -5e-130)
     t_3
     (if (<= t_2 4e+60)
       (fma (* 18.0 t) t_1 (- (* c b) (* 4.0 (fma a t (* i x)))))
       (if (<= t_2 1e+242) t_3 (- (* -4.0 (* a t)) 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 = (z * y) * x;
	double t_2 = (j * 27.0) * k;
	double t_3 = fma((-4.0 * a), t, fma((t_1 * t), 18.0, (c * b))) - t_2;
	double tmp;
	if (t_2 <= -5e-130) {
		tmp = t_3;
	} else if (t_2 <= 4e+60) {
		tmp = fma((18.0 * t), t_1, ((c * b) - (4.0 * fma(a, t, (i * x)))));
	} else if (t_2 <= 1e+242) {
		tmp = t_3;
	} else {
		tmp = (-4.0 * (a * t)) - 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(z * y) * x)
	t_2 = Float64(Float64(j * 27.0) * k)
	t_3 = Float64(fma(Float64(-4.0 * a), t, fma(Float64(t_1 * t), 18.0, Float64(c * b))) - t_2)
	tmp = 0.0
	if (t_2 <= -5e-130)
		tmp = t_3;
	elseif (t_2 <= 4e+60)
		tmp = fma(Float64(18.0 * t), t_1, Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))));
	elseif (t_2 <= 1e+242)
		tmp = t_3;
	else
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - t_2);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(-4.0 * a), $MachinePrecision] * t + N[(N[(t$95$1 * t), $MachinePrecision] * 18.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-130], t$95$3, If[LessEqual[t$95$2, 4e+60], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+242], t$95$3, N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.9999999999999996e-130 or 3.9999999999999998e60 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.00000000000000005e242

   1. Initial program 84.8%

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

   2. Taylor expanded in i around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 76.3

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

   4. Applied rewrites 76.3%

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

   if -4.9999999999999996e-130 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 3.9999999999999998e60

   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 j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 86.3

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

   4. Applied rewrites 86.3%

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

   if 1.00000000000000005e242 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 84.8%

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

   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 46.8

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

   4. Applied rewrites 46.8%

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

Alternative 6: 78.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, c \cdot b - 4 \cdot \mathsf{fma}\left(a, t, i \cdot x\right)\right)\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* 18.0 t) (* (* z y) x) (- (* c b) (* 4.0 (fma a t (* i x)))))))
   (if (<= t -5.9e-98)
     t_1
     (if (<= t 1.85e+18)
       (- (fma c b (* (* -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((18.0 * t), ((z * y) * x), ((c * b) - (4.0 * fma(a, t, (i * x)))));
	double tmp;
	if (t <= -5.9e-98) {
		tmp = t_1;
	} else if (t <= 1.85e+18) {
		tmp = fma(c, b, ((-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 = fma(Float64(18.0 * t), Float64(Float64(z * y) * x), Float64(Float64(c * b) - Float64(4.0 * fma(a, t, Float64(i * x)))))
	tmp = 0.0
	if (t <= -5.9e-98)
		tmp = t_1;
	elseif (t <= 1.85e+18)
		tmp = Float64(fma(c, b, 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[(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]}, If[LessEqual[t, -5.9e-98], t$95$1, If[LessEqual[t, 1.85e+18], N[(N[(c * b + N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.89999999999999991e-98 or 1.85e18 < t

   1. Initial program 84.6%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 76.7

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

   4. Applied rewrites 76.7%

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

   if -5.89999999999999991e-98 < t < 1.85e18

   1. Initial program 85.5%

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

   2. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 79.7

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

   4. Applied rewrites 79.7%

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

Alternative 7: 73.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot t, \left(z \cdot y\right) \cdot x, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* 18.0 t) (* (* z y) x) (* (fma i x (* a t)) -4.0))))
   (if (<= t -4.1e-29)
     t_1
     (if (<= t 1.85e+18)
       (- (fma c b (* (* -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((18.0 * t), ((z * y) * x), (fma(i, x, (a * t)) * -4.0));
	double tmp;
	if (t <= -4.1e-29) {
		tmp = t_1;
	} else if (t <= 1.85e+18) {
		tmp = fma(c, b, ((-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 = fma(Float64(18.0 * t), Float64(Float64(z * y) * x), Float64(fma(i, x, Float64(a * t)) * -4.0))
	tmp = 0.0
	if (t <= -4.1e-29)
		tmp = t_1;
	elseif (t <= 1.85e+18)
		tmp = Float64(fma(c, b, 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[(18.0 * t), $MachinePrecision] * N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e-29], t$95$1, If[LessEqual[t, 1.85e+18], N[(N[(c * b + N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0999999999999998e-29 or 1.85e18 < t

   1. Initial program 84.3%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 77.8

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 68.8

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

   7. Applied rewrites 68.8%

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

   if -4.0999999999999998e-29 < t < 1.85e18

   1. Initial program 85.8%

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

   2. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 79.0

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

   4. Applied rewrites 79.0%

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

Alternative 8: 72.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+67}:\\ \;\;\;\;\left(\left(a \cdot t\right) \cdot -4 - \left(x \cdot 4\right) \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)))
   (if (<= t -6e-18)
     t_1
     (if (<= t 2.9e-73)
       (- (fma c b (* (* -4.0 i) x)) (* (* j 27.0) k))
       (if (<= t 2.3e+67)
         (- (- (* (* a t) -4.0) (* (* x 4.0) i)) (* j (* k 27.0)))
         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(((z * y) * x), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -6e-18) {
		tmp = t_1;
	} else if (t <= 2.9e-73) {
		tmp = fma(c, b, ((-4.0 * i) * x)) - ((j * 27.0) * k);
	} else if (t <= 2.3e+67) {
		tmp = (((a * t) * -4.0) - ((x * 4.0) * i)) - (j * (k * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -6e-18)
		tmp = t_1;
	elseif (t <= 2.9e-73)
		tmp = Float64(fma(c, b, Float64(Float64(-4.0 * i) * x)) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 2.3e+67)
		tmp = Float64(Float64(Float64(Float64(a * t) * -4.0) - Float64(Float64(x * 4.0) * i)) - Float64(j * Float64(k * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e-18], t$95$1, If[LessEqual[t, 2.9e-73], N[(N[(c * b + N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+67], N[(N[(N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999966e-18 or 2.2999999999999999e67 < t

   1. Initial program 83.8%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 66.8

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

   4. Applied rewrites 66.8%

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

   if -5.99999999999999966e-18 < t < 2.9e-73

   1. Initial program 85.2%

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

   2. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 81.1

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

   4. Applied rewrites 81.1%

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

   if 2.9e-73 < t < 2.2999999999999999e67

   1. Initial program 89.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 89.4

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

   3. Applied rewrites 89.4%

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

   4. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 59.1

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

   6. Applied rewrites 59.1%

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

Alternative 9: 72.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x\right) - t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+67}:\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)))
   (if (<= t -6e-18)
     t_2
     (if (<= t 2.9e-73)
       (- (fma c b (* (* -4.0 i) x)) t_1)
       (if (<= t 2.3e+67) (- (- (* -4.0 (* a t)) (* (* x 4.0) i)) 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 = fma(((z * y) * x), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -6e-18) {
		tmp = t_2;
	} else if (t <= 2.9e-73) {
		tmp = fma(c, b, ((-4.0 * i) * x)) - t_1;
	} else if (t <= 2.3e+67) {
		tmp = ((-4.0 * (a * t)) - ((x * 4.0) * i)) - 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(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -6e-18)
		tmp = t_2;
	elseif (t <= 2.9e-73)
		tmp = Float64(fma(c, b, Float64(Float64(-4.0 * i) * x)) - t_1);
	elseif (t <= 2.3e+67)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(x * 4.0) * i)) - t_1);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e-18], t$95$2, If[LessEqual[t, 2.9e-73], N[(N[(c * b + N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 2.3e+67], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999966e-18 or 2.2999999999999999e67 < t

   1. Initial program 83.8%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 66.8

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

   4. Applied rewrites 66.8%

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

   if -5.99999999999999966e-18 < t < 2.9e-73

   1. Initial program 85.2%

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

   2. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 81.1

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

   4. Applied rewrites 81.1%

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

   if 2.9e-73 < t < 2.2999999999999999e67

   1. Initial program 89.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 59.3

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

   4. Applied rewrites 59.3%

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

Alternative 10: 72.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* z y) x) 18.0 (* -4.0 a)) t)))
   (if (<= t -6e-18)
     t_1
     (if (<= t 1.8e+67) (- (fma c b (* (* -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(((z * y) * x), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -6e-18) {
		tmp = t_1;
	} else if (t <= 1.8e+67) {
		tmp = fma(c, b, ((-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(z * y) * x), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -6e-18)
		tmp = t_1;
	elseif (t <= 1.8e+67)
		tmp = Float64(fma(c, b, 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[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e-18], t$95$1, If[LessEqual[t, 1.8e+67], N[(N[(c * b + N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.99999999999999966e-18 or 1.7999999999999999e67 < t

   1. Initial program 83.8%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 66.8

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

   4. Applied rewrites 66.8%

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

   if -5.99999999999999966e-18 < t < 1.7999999999999999e67

   1. Initial program 86.1%

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

   2. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 77.1

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

   4. Applied rewrites 77.1%

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

Alternative 11: 72.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)))
   (if (<= t -6e-18)
     t_1
     (if (<= t 1.8e+67) (fma -27.0 (* j k) (fma (* -4.0 i) x (* b c))) 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(((z * y) * x), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -6e-18) {
		tmp = t_1;
	} else if (t <= 1.8e+67) {
		tmp = fma(-27.0, (j * k), fma((-4.0 * i), x, (b * c)));
	} 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(z * y) * x), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -6e-18)
		tmp = t_1;
	elseif (t <= 1.8e+67)
		tmp = fma(-27.0, Float64(j * k), fma(Float64(-4.0 * i), x, Float64(b * c)));
	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[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e-18], t$95$1, If[LessEqual[t, 1.8e+67], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(N[(-4.0 * i), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.99999999999999966e-18 or 1.7999999999999999e67 < t

   1. Initial program 83.8%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 66.8

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

   4. Applied rewrites 66.8%

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

   if -5.99999999999999966e-18 < t < 1.7999999999999999e67

   1. Initial program 86.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 86.1

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

   3. Applied rewrites 86.1%

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

   4. Taylor expanded in a around -inf

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

   6. Applied rewrites 74.9%

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

   7. Taylor expanded in t around 0

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

      1. associate--r+ N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-*.f64 77.2

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

   9. Applied rewrites 77.2%

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

Alternative 12: 68.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := -4 \cdot \left(a \cdot t\right) - t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+249}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i, x, a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* a t)) t_1)))
   (if (<= t_1 -2e+249)
     t_2
     (if (<= t_1 2e+102) (fma c b (* (fma i x (* a t)) -4.0)) 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 * (a * t)) - t_1;
	double tmp;
	if (t_1 <= -2e+249) {
		tmp = t_2;
	} else if (t_1 <= 2e+102) {
		tmp = fma(c, b, (fma(i, x, (a * t)) * -4.0));
	} 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(-4.0 * Float64(a * t)) - t_1)
	tmp = 0.0
	if (t_1 <= -2e+249)
		tmp = t_2;
	elseif (t_1 <= 2e+102)
		tmp = fma(c, b, Float64(fma(i, x, Float64(a * t)) * -4.0));
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+249], t$95$2, If[LessEqual[t$95$1, 2e+102], N[(c * b + N[(N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999998e249 or 1.99999999999999995e102 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.0%

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

   2. Taylor expanded in 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 68.1

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

   4. Applied rewrites 68.1%

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

   if -1.9999999999999998e249 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.99999999999999995e102

   1. Initial program 87.2%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 68.7

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

   7. Applied rewrites 68.7%

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

Alternative 13: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot x\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-268}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -6.6e+88)
   (* (* (* z y) x) (* t 18.0))
   (if (<= t 4e-268)
     (- (* c b) (* j (* k 27.0)))
     (if (<= t 5.2e+51)
       (- (* (* -4.0 i) x) (* (* j 27.0) k))
       (fma (* a t) -4.0 (* c b))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.6e+88) {
		tmp = ((z * y) * x) * (t * 18.0);
	} else if (t <= 4e-268) {
		tmp = (c * b) - (j * (k * 27.0));
	} else if (t <= 5.2e+51) {
		tmp = ((-4.0 * i) * x) - ((j * 27.0) * k);
	} else {
		tmp = fma((a * t), -4.0, (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -6.6e+88)
		tmp = Float64(Float64(Float64(z * y) * x) * Float64(t * 18.0));
	elseif (t <= 4e-268)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	elseif (t <= 5.2e+51)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(Float64(j * 27.0) * k));
	else
		tmp = fma(Float64(a * t), -4.0, Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -6.6e+88], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-268], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+51], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.6000000000000006e88

   1. Initial program 82.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-*.f64 44.1

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

   6. Applied rewrites 44.1%

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

   if -6.6000000000000006e88 < t < 3.99999999999999983e-268

   1. Initial program 85.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.5

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

   3. Applied rewrites 85.5%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 51.6

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

   6. Applied rewrites 51.6%

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

   if 3.99999999999999983e-268 < t < 5.2000000000000002e51

   1. Initial program 87.8%

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

   2. Taylor expanded in 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 50.5

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

   4. Applied rewrites 50.5%

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

   if 5.2000000000000002e51 < t

   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 j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 77.2

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 47.5

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

   7. Applied rewrites 47.5%

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

Alternative 14: 50.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot x\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-73}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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
 (if (<= t -6.6e+88)
   (* (* (* z y) x) (* t 18.0))
   (if (<= t 8.6e-73)
     (- (* c b) (* j (* k 27.0)))
     (- (* -4.0 (* a t)) (* (* j 27.0) 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 tmp;
	if (t <= -6.6e+88) {
		tmp = ((z * y) * x) * (t * 18.0);
	} else if (t <= 8.6e-73) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * 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) :: tmp
    if (t <= (-6.6d+88)) then
        tmp = ((z * y) * x) * (t * 18.0d0)
    else if (t <= 8.6d-73) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else
        tmp = ((-4.0d0) * (a * t)) - ((j * 27.0d0) * 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 tmp;
	if (t <= -6.6e+88) {
		tmp = ((z * y) * x) * (t * 18.0);
	} else if (t <= 8.6e-73) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * 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):
	tmp = 0
	if t <= -6.6e+88:
		tmp = ((z * y) * x) * (t * 18.0)
	elif t <= 8.6e-73:
		tmp = (c * b) - (j * (k * 27.0))
	else:
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * 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)
	tmp = 0.0
	if (t <= -6.6e+88)
		tmp = Float64(Float64(Float64(z * y) * x) * Float64(t * 18.0));
	elseif (t <= 8.6e-73)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	else
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - Float64(Float64(j * 27.0) * 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)
	tmp = 0.0;
	if (t <= -6.6e+88)
		tmp = ((z * y) * x) * (t * 18.0);
	elseif (t <= 8.6e-73)
		tmp = (c * b) - (j * (k * 27.0));
	else
		tmp = (-4.0 * (a * t)) - ((j * 27.0) * 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_] := If[LessEqual[t, -6.6e+88], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e-73], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6000000000000006e88

   1. Initial program 82.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-*.f64 44.1

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

   6. Applied rewrites 44.1%

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

   if -6.6000000000000006e88 < t < 8.5999999999999998e-73

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 85.9

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

   3. Applied rewrites 85.9%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 53.5

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

   6. Applied rewrites 53.5%

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

   if 8.5999999999999998e-73 < t

   1. Initial program 85.4%

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

   2. Taylor expanded in 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 45.4

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

   4. Applied rewrites 45.4%

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

Alternative 15: 49.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;\left(\left(z \cdot y\right) \cdot x\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -6.6e+88)
   (* (* (* z y) x) (* t 18.0))
   (if (<= t 5.4e+51)
     (- (* c b) (* j (* k 27.0)))
     (fma (* a t) -4.0 (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.6e+88) {
		tmp = ((z * y) * x) * (t * 18.0);
	} else if (t <= 5.4e+51) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = fma((a * t), -4.0, (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -6.6e+88)
		tmp = Float64(Float64(Float64(z * y) * x) * Float64(t * 18.0));
	elseif (t <= 5.4e+51)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	else
		tmp = fma(Float64(a * t), -4.0, Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -6.6e+88], N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+51], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6000000000000006e88

   1. Initial program 82.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-*.f64 44.1

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

   6. Applied rewrites 44.1%

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

   if -6.6000000000000006e88 < t < 5.39999999999999983e51

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 86.5

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

   3. Applied rewrites 86.5%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 52.0

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

   6. Applied rewrites 52.0%

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

   if 5.39999999999999983e51 < t

   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 j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 77.2

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 47.5

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

   7. Applied rewrites 47.5%

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

Alternative 16: 49.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+88}:\\ \;\;\;\;\left(z \cdot \left(y \cdot x\right)\right) \cdot \left(t \cdot 18\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -6.6e+88)
   (* (* z (* y x)) (* t 18.0))
   (if (<= t 5.4e+51)
     (- (* c b) (* j (* k 27.0)))
     (fma (* a t) -4.0 (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (t <= -6.6e+88) {
		tmp = (z * (y * x)) * (t * 18.0);
	} else if (t <= 5.4e+51) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = fma((a * t), -4.0, (c * b));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -6.6e+88)
		tmp = Float64(Float64(z * Float64(y * x)) * Float64(t * 18.0));
	elseif (t <= 5.4e+51)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	else
		tmp = fma(Float64(a * t), -4.0, Float64(c * b));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -6.6e+88], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+51], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6000000000000006e88

   1. Initial program 82.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 43.9

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

   4. Applied rewrites 43.9%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-*.f64 44.1

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

   6. Applied rewrites 44.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 44.0

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

   8. Applied rewrites 44.0%

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

   if -6.6000000000000006e88 < t < 5.39999999999999983e51

   1. Initial program 86.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 86.5

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

   3. Applied rewrites 86.5%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 52.0

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

   6. Applied rewrites 52.0%

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

   if 5.39999999999999983e51 < t

   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 j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 77.2

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 47.5

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

   7. Applied rewrites 47.5%

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

Alternative 17: 49.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* a t) -4.0 (* c b))))
   (if (<= t -1.35e-17)
     t_1
     (if (<= t 5.4e+51) (- (* c b) (* j (* k 27.0))) 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((a * t), -4.0, (c * b));
	double tmp;
	if (t <= -1.35e-17) {
		tmp = t_1;
	} else if (t <= 5.4e+51) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(a * t), -4.0, Float64(c * b))
	tmp = 0.0
	if (t <= -1.35e-17)
		tmp = t_1;
	elseif (t <= 5.4e+51)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-17], t$95$1, If[LessEqual[t, 5.4e+51], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3500000000000001e-17 or 5.39999999999999983e51 < t

   1. Initial program 84.0%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 77.8

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 46.2

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

   7. Applied rewrites 46.2%

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

   if -1.3500000000000001e-17 < t < 5.39999999999999983e51

   1. Initial program 86.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. 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 86.0

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

   3. Applied rewrites 86.0%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 54.4

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

   6. Applied rewrites 54.4%

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

Alternative 18: 49.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-27 \cdot k\right) \cdot j\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(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+249)
     t_1
     (if (<= t_2 2e+110) (fma (* a t) -4.0 (* 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+249) {
		tmp = t_1;
	} else if (t_2 <= 2e+110) {
		tmp = fma((a * t), -4.0, (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(Float64(-27.0 * k) * j)
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+249)
		tmp = t_1;
	elseif (t_2 <= 2e+110)
		tmp = fma(Float64(a * t), -4.0, Float64(c * b));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+249], t$95$1, If[LessEqual[t$95$2, 2e+110], N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.9999999999999998e249 or 2e110 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 78.8%

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

   2. Taylor expanded in j around 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 63.2

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

   4. Applied rewrites 63.2%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   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 63.2

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

   6. Applied rewrites 63.2%

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

   if -1.9999999999999998e249 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e110

   1. Initial program 87.2%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 80.6

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

   4. Applied rewrites 80.6%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 47.6

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

   7. Applied rewrites 47.6%

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

Alternative 19: 37.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+53}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -4 \cdot 10^{-187}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{+83}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2e+53)
   (* c b)
   (if (<= (* b c) -4e-187)
     (* -27.0 (* k j))
     (if (<= (* b c) 1e+83) (* -4.0 (* a t)) (* c b)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+53) {
		tmp = c * b;
	} else if ((b * c) <= -4e-187) {
		tmp = -27.0 * (k * j);
	} else if ((b * c) <= 1e+83) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-2d+53)) then
        tmp = c * b
    else if ((b * c) <= (-4d-187)) then
        tmp = (-27.0d0) * (k * j)
    else if ((b * c) <= 1d+83) then
        tmp = (-4.0d0) * (a * t)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+53) {
		tmp = c * b;
	} else if ((b * c) <= -4e-187) {
		tmp = -27.0 * (k * j);
	} else if ((b * c) <= 1e+83) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2e+53:
		tmp = c * b
	elif (b * c) <= -4e-187:
		tmp = -27.0 * (k * j)
	elif (b * c) <= 1e+83:
		tmp = -4.0 * (a * t)
	else:
		tmp = c * b
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+53)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -4e-187)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (Float64(b * c) <= 1e+83)
		tmp = Float64(-4.0 * Float64(a * t));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2e+53)
		tmp = c * b;
	elseif ((b * c) <= -4e-187)
		tmp = -27.0 * (k * j);
	elseif ((b * c) <= 1e+83)
		tmp = -4.0 * (a * t);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+53], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -4e-187], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+83], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2e53 or 1.00000000000000003e83 < (*.f64 b c)

   1. Initial program 82.0%

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

   2. Taylor expanded in 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 49.9

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

   4. Applied rewrites 49.9%

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

   if -2e53 < (*.f64 b c) < -4.0000000000000001e-187

   1. Initial program 86.2%

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

   2. Taylor expanded in j around 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 28.8

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

   4. Applied rewrites 28.8%

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

   if -4.0000000000000001e-187 < (*.f64 b c) < 1.00000000000000003e83

   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

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 26.2

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

   4. Applied rewrites 26.2%

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

Alternative 20: 36.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e+129) t_1 (if (<= t_2 2e+110) (* 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 <= -5e+129) {
		tmp = t_1;
	} else if (t_2 <= 2e+110) {
		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 <= (-5d+129)) then
        tmp = t_1
    else if (t_2 <= 2d+110) 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 <= -5e+129) {
		tmp = t_1;
	} else if (t_2 <= 2e+110) {
		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 <= -5e+129:
		tmp = t_1
	elif t_2 <= 2e+110:
		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 <= -5e+129)
		tmp = t_1;
	elseif (t_2 <= 2e+110)
		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 <= -5e+129)
		tmp = t_1;
	elseif (t_2 <= 2e+110)
		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, -5e+129], t$95$1, If[LessEqual[t$95$2, 2e+110], N[(c * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000003e129 or 2e110 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   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 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 58.1

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

   4. Applied rewrites 58.1%

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

   if -5.0000000000000003e129 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e110

   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 27.1

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

   4. Applied rewrites 27.1%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 23.2% 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 85.0%

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

2. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 23.2

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

4. Applied rewrites 23.2%

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

Reproduce

herbie shell --seed 2025117 
(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)))