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

Percentage Accurate: 85.4% → 92.8%

Time: 6.5s

Alternatives: 17

Speedup: 0.5×

• 50.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.8% accurate, 0.5× speedup

Math

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

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))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY) t_1 (* (fma (* (* t z) 18.0) y (* 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)) - ((j * 27.0) * k);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(((t * z) * 18.0), y, (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(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(Float64(t * z) * 18.0), y, 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[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + 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 85.4%

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

   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 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 43.6

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

   6. Applied rewrites 43.6%

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

Alternative 2: 92.7% accurate, 0.5× speedup

Math

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

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)))
   (if (<=
        (-
         (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) t_1)
         t_2)
        INFINITY)
     (- (- (fma c b (* (fma (* (* x y) z) 18.0 (* -4.0 a)) t)) t_1) t_2)
     (* (fma (* (* t z) 18.0) y (* 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 tmp;
	if (((((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - t_1) - t_2) <= ((double) INFINITY)) {
		tmp = (fma(c, b, (fma(((x * y) * z), 18.0, (-4.0 * a)) * t)) - t_1) - t_2;
	} else {
		tmp = fma(((t * z) * 18.0), y, (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)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - t_1) - t_2) <= Inf)
		tmp = Float64(Float64(fma(c, b, Float64(fma(Float64(Float64(x * y) * z), 18.0, Float64(-4.0 * a)) * t)) - t_1) - t_2);
	else
		tmp = Float64(fma(Float64(Float64(t * z) * 18.0), y, 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]}, If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], Infinity], N[(N[(N[(c * b + N[(N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + 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 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

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   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 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 43.6

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

   6. Applied rewrites 43.6%

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

Alternative 3: 82.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, a \cdot -4\right), t, b \cdot c\right)\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot i, x, \mathsf{fma}\left(c, b, \left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t\right) \cdot 18\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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
          (* k j)
          -27.0
          (fma (fma (* (* y x) z) 18.0 (* a -4.0)) t (* b c)))))
   (if (<= a -4.2e-39)
     t_1
     (if (<= a 2.5e+14)
       (-
        (fma (* -4.0 i) x (fma c b (* (* (* (* y z) x) t) 18.0)))
        (* (* 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((k * j), -27.0, fma(fma(((y * x) * z), 18.0, (a * -4.0)), t, (b * c)));
	double tmp;
	if (a <= -4.2e-39) {
		tmp = t_1;
	} else if (a <= 2.5e+14) {
		tmp = fma((-4.0 * i), x, fma(c, b, ((((y * z) * x) * t) * 18.0))) - ((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(k * j), -27.0, fma(fma(Float64(Float64(y * x) * z), 18.0, Float64(a * -4.0)), t, Float64(b * c)))
	tmp = 0.0
	if (a <= -4.2e-39)
		tmp = t_1;
	elseif (a <= 2.5e+14)
		tmp = Float64(fma(Float64(-4.0 * i), x, fma(c, b, Float64(Float64(Float64(Float64(y * z) * x) * t) * 18.0))) - 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[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-39], t$95$1, If[LessEqual[a, 2.5e+14], N[(N[(N[(-4.0 * i), $MachinePrecision] * x + N[(c * b + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.19999999999999987e-39 or 2.5e14 < a

   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

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 75.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 77.0

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

   10. Applied rewrites 77.0%

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

   if -4.19999999999999987e-39 < a < 2.5e14

   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 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

   6. Applied rewrites 74.8%

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

Alternative 4: 82.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, a \cdot -4\right), t, b \cdot c\right)\right)\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-113}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* k j)
          -27.0
          (fma (fma (* (* y x) z) 18.0 (* a -4.0)) t (* b c)))))
   (if (<= t -2.75e-161)
     t_1
     (if (<= t 2.8e-113) (- (* c b) (fma (* i x) 4.0 (* (* k j) 27.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((k * j), -27.0, fma(fma(((y * x) * z), 18.0, (a * -4.0)), t, (b * c)));
	double tmp;
	if (t <= -2.75e-161) {
		tmp = t_1;
	} else if (t <= 2.8e-113) {
		tmp = (c * b) - fma((i * x), 4.0, ((k * j) * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * j), -27.0, fma(fma(Float64(Float64(y * x) * z), 18.0, Float64(a * -4.0)), t, Float64(b * c)))
	tmp = 0.0
	if (t <= -2.75e-161)
		tmp = t_1;
	elseif (t <= 2.8e-113)
		tmp = Float64(Float64(c * b) - fma(Float64(i * x), 4.0, Float64(Float64(k * j) * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.75e-161], t$95$1, If[LessEqual[t, 2.8e-113], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.75e-161 or 2.8e-113 < 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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 75.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 77.0

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

   10. Applied rewrites 77.0%

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

   if -2.75e-161 < t < 2.8e-113

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

Alternative 5: 82.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\right)\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-80}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* k j)
          -27.0
          (fma c b (* (fma (* (* z y) x) 18.0 (* -4.0 a)) t)))))
   (if (<= t -2e-177)
     t_1
     (if (<= t 8e-80) (- (* c b) (fma (* i x) 4.0 (* (* k j) 27.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((k * j), -27.0, fma(c, b, (fma(((z * y) * x), 18.0, (-4.0 * a)) * t)));
	double tmp;
	if (t <= -2e-177) {
		tmp = t_1;
	} else if (t <= 8e-80) {
		tmp = (c * b) - fma((i * x), 4.0, ((k * j) * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * j), -27.0, fma(c, b, Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * t)))
	tmp = 0.0
	if (t <= -2e-177)
		tmp = t_1;
	elseif (t <= 8e-80)
		tmp = Float64(Float64(c * b) - fma(Float64(i * x), 4.0, Float64(Float64(k * j) * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * j), $MachinePrecision] * -27.0 + N[(c * b + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-177], t$95$1, If[LessEqual[t, 8e-80], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e-177 or 7.99999999999999969e-80 < 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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 75.7%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. *-commutative N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

   10. Applied rewrites 76.5%

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

   if -1.9999999999999999e-177 < t < 7.99999999999999969e-80

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

Alternative 6: 73.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-\mathsf{fma}\left(-18, \left(y \cdot z\right) \cdot t, i \cdot 4\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -18.0 (* (* y z) t) (* i 4.0)) x)) (* (* j 27.0) k))))
   (if (<= x -4.5e+65)
     t_1
     (if (<= x 4.4e+152) (fma (* t a) -4.0 (fma (* k j) -27.0 (* 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(-18.0, ((y * z) * t), (i * 4.0)) * x) - ((j * 27.0) * k);
	double tmp;
	if (x <= -4.5e+65) {
		tmp = t_1;
	} else if (x <= 4.4e+152) {
		tmp = fma((t * a), -4.0, fma((k * j), -27.0, (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(Float64(-Float64(fma(-18.0, Float64(Float64(y * z) * t), Float64(i * 4.0)) * x)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (x <= -4.5e+65)
		tmp = t_1;
	elseif (x <= 4.4e+152)
		tmp = fma(Float64(t * a), -4.0, fma(Float64(k * j), -27.0, 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[(-18.0 * N[(N[(y * z), $MachinePrecision] * t), $MachinePrecision] + N[(i * 4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]) - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+65], t$95$1, If[LessEqual[x, 4.4e+152], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5e65 or 4.3999999999999996e152 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in a around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. metadata-eval N/A

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

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

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

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

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 59.7

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

   7. Applied rewrites 59.7%

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

   if -4.5e65 < x < 4.3999999999999996e152

   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

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 60.5%

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

Alternative 7: 71.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot x\right) \cdot 18, t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 c b (* -4.0 (* a t))) (* (* j 27.0) k))))
   (if (<= a -9.8e-36)
     t_1
     (if (<= a 5.2e+38)
       (fma (* k j) -27.0 (fma (* (* (* z y) x) 18.0) t (* 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(c, b, (-4.0 * (a * t))) - ((j * 27.0) * k);
	double tmp;
	if (a <= -9.8e-36) {
		tmp = t_1;
	} else if (a <= 5.2e+38) {
		tmp = fma((k * j), -27.0, fma((((z * y) * x) * 18.0), t, (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(c, b, Float64(-4.0 * Float64(a * t))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (a <= -9.8e-36)
		tmp = t_1;
	elseif (a <= 5.2e+38)
		tmp = fma(Float64(k * j), -27.0, fma(Float64(Float64(Float64(z * y) * x) * 18.0), t, 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[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e-36], t$95$1, If[LessEqual[a, 5.2e+38], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9.7999999999999994e-36 or 5.1999999999999998e38 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in x around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.9

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

   4. Applied rewrites 60.9%

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

   if -9.7999999999999994e-36 < a < 5.1999999999999998e38

   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

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 75.7%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lift-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lift-*.f64 60.5

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

   11. Applied rewrites 60.5%

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

Alternative 8: 68.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, i \cdot -4\right) \cdot x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(t \cdot a, -4, \mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.3e+36)
   (* (fma (* (* t z) 18.0) y (* i -4.0)) x)
   (if (<= x 1.75e+153)
     (fma (* t a) -4.0 (fma (* k j) -27.0 (* b c)))
     (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.3e+36) {
		tmp = fma(((t * z) * 18.0), y, (i * -4.0)) * x;
	} else if (x <= 1.75e+153) {
		tmp = fma((t * a), -4.0, fma((k * j), -27.0, (b * c)));
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.3e+36)
		tmp = Float64(fma(Float64(Float64(t * z) * 18.0), y, Float64(i * -4.0)) * x);
	elseif (x <= 1.75e+153)
		tmp = fma(Float64(t * a), -4.0, fma(Float64(k * j), -27.0, Float64(b * c)));
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.3e+36], N[(N[(N[(N[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.75e+153], N[(N[(t * a), $MachinePrecision] * -4.0 + N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3000000000000001e36

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 43.6

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

   6. Applied rewrites 43.6%

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

   if -1.3000000000000001e36 < x < 1.75e153

   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

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

      2. lift-+.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

   3. Applied rewrites 88.0%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 60.5%

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

   if 1.75e153 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

Alternative 9: 58.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y \cdot z\right) \cdot x, 18, a \cdot -4\right) \cdot t\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* (* y z) x) 18.0 (* a -4.0)) t)))
   (if (<= t -9.2e-110)
     t_1
     (if (<= t 5.4e-85) (- (* b c) (* (* j 27.0) k)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(((y * z) * x), 18.0, (a * -4.0)) * t;
	double tmp;
	if (t <= -9.2e-110) {
		tmp = t_1;
	} else if (t <= 5.4e-85) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(Float64(y * z) * x), 18.0, Float64(a * -4.0)) * t)
	tmp = 0.0
	if (t <= -9.2e-110)
		tmp = t_1;
	elseif (t <= 5.4e-85)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -9.2e-110], t$95$1, If[LessEqual[t, 5.4e-85], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.2000000000000006e-110 or 5.4000000000000003e-85 < 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 j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 24.2

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

   4. Applied rewrites 24.2%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

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

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-*.f64 42.7

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

   7. Applied rewrites 42.7%

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

   if -9.2000000000000006e-110 < t < 5.4000000000000003e-85

   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 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

Alternative 10: 58.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t \cdot z\right) \cdot 18, y, i \cdot -4\right) \cdot x\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* t z) 18.0) y (* i -4.0)) x)))
   (if (<= x -2.65e-59)
     t_1
     (if (<= x 1.9e+103) (fma (* k j) -27.0 (* 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(((t * z) * 18.0), y, (i * -4.0)) * x;
	double tmp;
	if (x <= -2.65e-59) {
		tmp = t_1;
	} else if (x <= 1.9e+103) {
		tmp = fma((k * j), -27.0, (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(t * z) * 18.0), y, Float64(i * -4.0)) * x)
	tmp = 0.0
	if (x <= -2.65e-59)
		tmp = t_1;
	elseif (x <= 1.9e+103)
		tmp = fma(Float64(k * j), -27.0, 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[(t * z), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.65e-59], t$95$1, If[LessEqual[x, 1.9e+103], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6500000000000002e-59 or 1.8999999999999998e103 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 43.6

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

   6. Applied rewrites 43.6%

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

   if -2.6500000000000002e-59 < x < 1.8999999999999998e103

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

Alternative 11: 57.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* 18.0 t) (* z y) (* -4.0 i)) x)))
   (if (<= x -2.6e-59)
     t_1
     (if (<= x 1.2e+126) (fma (* k j) -27.0 (* 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((18.0 * t), (z * y), (-4.0 * i)) * x;
	double tmp;
	if (x <= -2.6e-59) {
		tmp = t_1;
	} else if (x <= 1.2e+126) {
		tmp = fma((k * j), -27.0, (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(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x)
	tmp = 0.0
	if (x <= -2.6e-59)
		tmp = t_1;
	elseif (x <= 1.2e+126)
		tmp = fma(Float64(k * j), -27.0, 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[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.6e-59], t$95$1, If[LessEqual[x, 1.2e+126], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.59999999999999998e-59 or 1.20000000000000006e126 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

   if -2.59999999999999998e-59 < x < 1.20000000000000006e126

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

Alternative 12: 48.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(y \cdot x\right) \cdot t\right) \cdot 18\right) \cdot z\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-247}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-154}:\\ \;\;\;\;-\mathsf{fma}\left(4 \cdot x, i, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* (* y x) t) 18.0) z)))
   (if (<= z -2.7e-29)
     t_1
     (if (<= z -9.5e-247)
       (- (* b c) (* (* j 27.0) k))
       (if (<= z 2.2e-154)
         (- (fma (* 4.0 x) i (* (* k j) 27.0)))
         (if (<= z 8.1e+108) (fma (* k j) -27.0 (* 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 = (((y * x) * t) * 18.0) * z;
	double tmp;
	if (z <= -2.7e-29) {
		tmp = t_1;
	} else if (z <= -9.5e-247) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (z <= 2.2e-154) {
		tmp = -fma((4.0 * x), i, ((k * j) * 27.0));
	} else if (z <= 8.1e+108) {
		tmp = fma((k * j), -27.0, (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(Float64(Float64(Float64(y * x) * t) * 18.0) * z)
	tmp = 0.0
	if (z <= -2.7e-29)
		tmp = t_1;
	elseif (z <= -9.5e-247)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (z <= 2.2e-154)
		tmp = Float64(-fma(Float64(4.0 * x), i, Float64(Float64(k * j) * 27.0)));
	elseif (z <= 8.1e+108)
		tmp = fma(Float64(k * j), -27.0, 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[(y * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -2.7e-29], t$95$1, If[LessEqual[z, -9.5e-247], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-154], (-N[(N[(4.0 * x), $MachinePrecision] * i + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 8.1e+108], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.70000000000000023e-29 or 8.1e108 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 37.9

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

   7. Applied rewrites 37.9%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 20.1

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

   10. Applied rewrites 20.1%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 27.6

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

   13. Applied rewrites 27.6%

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

   if -2.70000000000000023e-29 < z < -9.49999999999999939e-247

   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 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

   if -9.49999999999999939e-247 < z < 2.20000000000000007e-154

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in b around 0

      \[\leadsto -1 \cdot \color{blue}{\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-*.f64 42.7

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

   7. Applied rewrites 42.7%

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

   if 2.20000000000000007e-154 < z < 8.1e108

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

Alternative 13: 47.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(y \cdot x\right) \cdot t\right) \cdot 18\right) \cdot z\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* (* (* y x) t) 18.0) z)))
   (if (<= x -1.2e+36)
     t_1
     (if (<= x 7.5e+153) (fma (* k j) -27.0 (* 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 = (((y * x) * t) * 18.0) * z;
	double tmp;
	if (x <= -1.2e+36) {
		tmp = t_1;
	} else if (x <= 7.5e+153) {
		tmp = fma((k * j), -27.0, (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(Float64(Float64(Float64(y * x) * t) * 18.0) * z)
	tmp = 0.0
	if (x <= -1.2e+36)
		tmp = t_1;
	elseif (x <= 7.5e+153)
		tmp = fma(Float64(k * j), -27.0, 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[(y * x), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -1.2e+36], t$95$1, If[LessEqual[x, 7.5e+153], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999996e36 or 7.50000000000000065e153 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. associate-*r* N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 43.0

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

   4. Applied rewrites 43.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 37.9

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

   7. Applied rewrites 37.9%

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

   8. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 20.1

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

   10. Applied rewrites 20.1%

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

   11. Taylor expanded in y around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. *-commutative N/A

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

       4. lower-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 27.6

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

   13. Applied rewrites 27.6%

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

   if -1.19999999999999996e36 < x < 7.50000000000000065e153

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

Alternative 14: 47.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(-4 \cdot i\right) \cdot x\\ \mathbf{if}\;i \leq -1.35 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 10^{+131}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (* (* -4.0 i) x)))
   (if (<= i -1.35e+207)
     t_1
     (if (<= i 1e+131) (fma (* k j) -27.0 (* 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 = (-4.0 * i) * x;
	double tmp;
	if (i <= -1.35e+207) {
		tmp = t_1;
	} else if (i <= 1e+131) {
		tmp = fma((k * j), -27.0, (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(Float64(-4.0 * i) * x)
	tmp = 0.0
	if (i <= -1.35e+207)
		tmp = t_1;
	elseif (i <= 1e+131)
		tmp = fma(Float64(k * j), -27.0, 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[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[i, -1.35e+207], t$95$1, If[LessEqual[i, 1e+131], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.35000000000000012e207 or 9.9999999999999991e130 < i

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 21.6

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

   4. Applied rewrites 21.6%

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

   if -1.35000000000000012e207 < i < 9.9999999999999991e130

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around 0

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-*.f64 43.8

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

   7. Applied rewrites 43.8%

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

Alternative 15: 36.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+97}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+65}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot k\right) \cdot j\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+97)
     (* -27.0 (* k j))
     (if (<= t_1 2e+65) (* (* -4.0 i) x) (* (* -27.0 k) j)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+97) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 2e+65) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Fortran

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

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

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= (-2d+97)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= 2d+65) then
        tmp = ((-4.0d0) * i) * x
    else
        tmp = ((-27.0d0) * k) * j
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+97) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 2e+65) {
		tmp = (-4.0 * i) * x;
	} else {
		tmp = (-27.0 * k) * j;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -2e+97:
		tmp = -27.0 * (k * j)
	elif t_1 <= 2e+65:
		tmp = (-4.0 * i) * x
	else:
		tmp = (-27.0 * k) * j
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -2e+97)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 2e+65)
		tmp = Float64(Float64(-4.0 * i) * x);
	else
		tmp = Float64(Float64(-27.0 * k) * j);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -2e+97)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 2e+65)
		tmp = (-4.0 * i) * x;
	else
		tmp = (-27.0 * k) * j;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+97], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+65], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.0000000000000001e97

   1. Initial program 85.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 24.2

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

   4. Applied rewrites 24.2%

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

   if -2.0000000000000001e97 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2e65

   1. Initial program 85.4%

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

   2. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 21.6

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

   4. Applied rewrites 21.6%

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

   if 2e65 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 24.2

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

   4. Applied rewrites 24.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 24.2

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

   6. Applied rewrites 24.2%

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

Alternative 16: 24.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \left(-27 \cdot k\right) \cdot j \end{array} \]

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 (* (* -27.0 k) j))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (-27.0 * k) * j;
}

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 = ((-27.0d0) * k) * j
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 (-27.0 * k) * j;
}

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 (-27.0 * k) * j

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(Float64(-27.0 * k) * j)
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 = (-27.0 * k) * j;
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[(N[(-27.0 * k), $MachinePrecision] * j), $MachinePrecision]

Derivation

1. Initial program 85.4%

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

2. Taylor expanded in j around inf

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

   1. lower-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 24.2

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

4. Applied rewrites 24.2%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*r* N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 24.2

      \[\leadsto \left(-27 \cdot k\right) \cdot j \]

6. Applied rewrites 24.2%

   \[\leadsto \left(-27 \cdot k\right) \cdot \color{blue}{j} \]
7. Add Preprocessing

Alternative 17: 24.2% accurate, 6.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ -27 \cdot \left(k \cdot j\right) \end{array} \]

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 (* -27.0 (* k j)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return -27.0 * (k * j);
}

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 = (-27.0d0) * (k * j)
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 -27.0 * (k * j);
}

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 -27.0 * (k * j)

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(-27.0 * Float64(k * j))
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 = -27.0 * (k * j);
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[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.4%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

2. Taylor expanded in j around inf

   \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

   2. *-commutative N/A

      \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   3. lower-*.f64 24.2

      \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

4. Applied rewrites 24.2%

   \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025139 
(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)))